We can generalize Frege's distinction between sense and reference, which were applied originally to singular terms (like proper names and definite descriptions), to cover other terms as well.  Corresponding to reference, philosophers talk about the EXTENSION of a general term.  The general (mass) term `water' has as its extension all the water in our world.  The general term `horse' has as its extension all the horses in the world.  Corresponding to Frege's sense, we can talk about the INTENSION of a general term.  The extension of `horse' in this world is a certain set of horses.  But this can change; and in another possible world, this extension is different (we may have a different set of horses.  The intension of `horse' is a function (in the mathematical sense) or a rule which determines the extension of the term in each possible world.  Now consider the following two expressions: `creature with a heart' and `creature with a kidney'. Intuitively, these expressions are not synonymous, they have different meanings.  But they, as a matter of fact, have the same extension (the same set of individuals in this world).  We can try to capture the intuition that they are not synonymous by noticing that they have different intensions (they pick out different sets of individuals in other worlds).  In this way, intensions can be seen at least to capture a very crucial element in the intuitive notion of meaning.
     Philosophers since Frege have held that the intension of a term determines its extension, so you couldn't have two expressions with different extensions which had the same intension (though you can have two expressions with different intensions but same extension.  People have also held that the intension of a term is the set of concepts (or beliefs) a user of the term `has in mind', or associates with the term.  We then get the following two theses:
     (i) `What's in a speaker's head' (a set of concepts, or beliefs) determines a term's intension
     (ii) intensions determine extension
Putnam argues that (i) and (ii) cannot be true together.
     Notice first that (i) and (ii) together imply that `what's in a speaker's head' (the beliefs/concepts the speaker associates with a term) determines the extension of the term in the speaker's language.  So if we had two individuals who were in the same psychological state - had the same beliefs/concepts associated with some term A which they both use - then the extension of the term A in their language would be the same: A would correctly apply to the same things.  Putnam develops an example to show that this is false: It is possible for two speakers to be in the same psychological state (and therefore have the same understanding of a term) and yet the term have different extensions in their respective idiolects.

Putnam's Twin Earth
     Putnam asks us to imagine a planet, he calls it "twin-earth", which is just like earth except that what they call `water' has the chemical structure XYZ, not H2O.  In other words, there is no water on twin-earth, even though they use the sound `water' to talk about some liquid that has all the superficial qualities (look, taste, location, etc.) of our water.  Now imagine that Oscar on Earth has an exact duplicate, twin-Oscar.  They have exactly the same beliefs `in their heads', everything looks the same to them from the inside - they both think that water is a colorless, tasteless odorless thirst-quenching liquid.  Yet the extensions of their respective uses of `water' are different: the sound `water' on Earth applies to a substance with the chemical structure H2O, on Twin-Earth it applies to a substance with chemical structure XYZ, and those are two different substances.  (Analogy: Imagine a world in which somebody looking exactly like George Bush happens to be also called "George Bush".  This would be a case where the name "George Bush" has different references - one person in this world, namely, George Bush, and another person in the imagined world - not our George Bush, but someone who happens to look like him.)
     If you think that one belief that Oscar on Earth has and which Twin-Oscar lacks is that water has chemical structure H2O, just go back in time to 1750, before chemical structure was discovered.  Oscar then would have had the same beliefs about water (in the sense of the same ideas running through his mind in connection with the word `water') as twin-Oscar - neither would have had beliefs about chemical structure. Still, Putnam argues, given that water and twin-water differ in chemical structure, the extension of the word `water' - what the word is true of, or correctly applies to - would have been different on Earth and on Twin-Earth.
     You might think that the extension of the word `water' has changed between 1750 and later, given that we have different beliefs about water from the beliefs people had before chemistry was developed.  This wouldn't be very plausible.  (This would be analogous to the claim that the set of descriptions associated with a name determine what the name refers to, so whoever fits the descriptions is the reference, and a change in the set of associated descriptions may lead to a change in the reference of the name.)  It seems more plausible to think that English speakers in 1750 and we today were talking about the same stuff, namely - water, it's just that with the advent of chemistry more truths were discovered about water.

     This suggests that the way the extension of a term is determined is not by its fitting a set of beliefs or descriptions.  If we and English speakers in 1750 could be said to talk about the same substance (water, or gold, or whatever) despite differences in our beliefs, something other than our beliefs must determine extension.  What could that be?  Putnam has an answer.  Think about the introduction of a term like `water' or `gold' or `horse' into the language.  When our ancestors named some liquid (metal, kind of animal) by saying "This is to be called `water' (`gold', `horse')", pointing to some sample of water (gold or horses), what they were doing could be thought of in the following way: they were really saying something like: "Let anything which is the same liquid (or metal, or kind of animal) as this sample be called `water' (`gold', `horse')."  Now, whether something is the same liquid as water may require scientific investigation to decide, and at the time of introduction of the word `water', people didn't even have the requisite scientific knowledge to determine it.  But it's whether or not something has the same internal structure as the sample is what determines the correctness of applying the relevant (natural-kind) term, and not whatever beliefs (or descriptions) users of the term associate with it.

     GO OVER PUTNAM'S EXAMPLE OF `aluminum' AND `molybdenum'.  (The point: If Oscar1 and Oscar2 are alike in not being metalurgists able to distinguish the two metals, they would not have any distinguishing beliefs about the two metals.  Yet the extensions of their terms would be switched.  This is because Oscar1's use of the term `aluminum' has been linked to aluminum, whereas Oscar2's use of the same sound `aluminum' has been linked rather to molybdenum.  A similar point may be made without considering Twin-Earth.  My own use of `elm' and `beech' is backed up by the same descriptions.  Yet the extension of the two terms is different; one applies to elms, the other to beeches.  If, using my rather general (non-distinguishing) beliefs, I were to call a beech `elm' I would be misapplying the term, even though the tree would fit the descriptions (or concept) I associate with `elm'.)

     Putnam concludes from all this that meanings ain't in the head:
 THE CONCEPTS AN INDIVIDUAL SPEAKER ASSOCIATES WITH A TERM DO NOT DETERMINE THE EXTENSION OF THE TERM.
Insofar that we think of meaning as that which determines extension, then meanings are not `in the head', they are not the concepts associated by individuals with terms.

     Terms like `gold', `aluminum', etc. exhibit what Putnam calls division of linguistic labor: not everyone who uses the term `gold' needs to have a method of recognizing whether something is gold.  Being a member in a linguistic community enables a speaker to use words in communication without possessing complete identifying knowledge of what the words correctly apply to.  A speaker can rely on experts and borrow the extension of terms from them, as it were (compare borrowing the reference of a name like "Feynman" from someone who knows who he is).  Just as not everyone who has an interest in gold things needs to know what gold is (can rely on experts for that) so not everyone who has a use for the word gold needs to associate with this word concepts (or descriptions) which allow him/her to apply the word correctly in every case.  In this sense, there is a social element in the determination of extension.  This means that what determines the extension of a word may not be known to most users of the word.  Putnam offers the following hypothesis (p.228):  Whenever a term is subject to the division of linguistic labor, the average speaker acquiring it doesn't acquire anything that fixes its extension.  (Not all words are subject to the division of linguistic labor; e.g.: `chair', `pain', `he', etc.  Every competent user of these terms is as much of an expert on their correct application as any other.)
     Now, it may be argued that by showing that the extension of (many) terms is not determined by what individual speakers associate with them, Putnam has not really completely discredited the view that intension determines extension.  For, it may be argued that expert knowledge (on which we, lay people, rely in our use of terms like `gold', `aluminum', `whale') constitutes `communal' intension, or concepts that are still `in the head', though not in the head of every speaker.  And, it may be argued, `communal' intension does still determine extension.
     But an example used before should convince us that this is not so, at least not with respect to natural kind terms.  Remember the English speaking community of 1750, prior to the advent of chemistry.  Noone in that community had the relevant expert knowledge to determine whether a piece of metal were really gold.  Indeed they may have been wrong about many of their applications of the term `gold', without being able to settle the matter.  Still, any piece of metal with atomic no. 79 was in the extension of their term `gold' (just as it is in ours, we speak the same language as they did).  It's just that they didn't have the expert means to decide conclusively whether that was so or not.  There are pieces of metal to which, perhaps, anyone in 1750 would have wrongly applied the term `gold'.  Such applications would have been in full conformity with what anyone at that time would have thought `gold' applied to, and yet those pieces of metal were not in the extension of `gold'.  This shows that even `community' intension doesn't determine extension.

Natural Kind Terms and Rigid Designation
     One way to express Putnam's conclusions about terms like `water', `horse', etc. is this: these terms are rigid designators.  Like proper names on Kripke's view, they designate (or apply to, or have as their extension) the same kind of stuff (liquid, metal) or animal in every possible world in which the relevant stuff or animal species exist.  Just as when we dub someone `Joe Egg', we intend to give a specific individual, the one in front of us, however described, the name `Joe Egg', so when we give an ostensive definition of a kind term (a definition which uses a demonstrative like `this stuff', pointing to a sample of water, or `that animal', pointing to a giraffe), we mean to label that kind of stuff or animal, whatever turns out to be true or it, by that term.  Of course, in another world, the same stuff, say aluminum, might have been named differently, just as George Bush might have been given a different name.  Still, when we consider that other world we are talking about aluminum - a certain metal with specific internal chemical structure, whatever its name is, and whatever its superficial characteristics are.  Conversely, we could have a metal with the same superficial qualities of aluminum, which is even called aluminum, but which isn't aluminum; being aluminum is not a matter of looking a certain way; rather it's a matter of having a certain chemical structure (and being a horse is not a matter of looking a certain way and being called `horse'; rather it's a matter of having a certain genetic structure).
     How is the extension of a natural kind term, then, determined?  Putnam says it's determined `indexically'.  Something is in the extension of `water' iff it bear the relation same-liquid to this stuff (that is, to the stuff original users of the term `water' pointed to.  When do x and y stand in the same-liquid relation?  On p. 238, Putnam says: (i) x and y must both be liquids; and (ii) x and y must agree in essential physical properties (they must share chemical structure, for instance.
     Putnam seems to be making about the term `water' (etc.) a similar claim to the one made by Kripke about the name `Nixon'.  What determines the extension of `water' is not a set of beliefs about water, just as what determines the reference of `Nixon' is not a set of descriptions believed to hold of Nixon.  What determines the extension of natural kind terms is a certain causal connection established in the introduction of the term into the language between uses of the term and a certain kind of thing (substance, animal) in the world.  In this respect, natural kind terms, for Putnam, are like names - the label natural kinds (liquids, elements, metals, species, etc.).  (Putnam thinks even non-natural kind terms like `pencil' work a bit like that.)

Putnam's Stereotypes
     Extension, Putnam argues, is not fixed by what's in anyone's head; it is fixed socially and indexically.  To find out the correct extension of a term, it's not enough to think hard about the concepts we ourselves associate with the term.  It may not even be enough to ask experts about the concepts they associate with the term.  We, even as a community, may lack the expert knowledge required to determine the correct extension of our terms.  What determines correct extension depends on the world - which things bear sameness relations to the things caught up in the original ostensive definitions of our terms.  This is true for natural (and some non-natural) kind terms, as well as for proper names.
     But there is, for Putnam, an important difference between general terms like `gold' and `pencil' and proper names.  With respect to the former, but not with respect to the latter, there is minimal competence requirement: a competent user of a term like `water' must associate with the term certain standard beliefs - which Putnam calls `stereotypes' - that it's odorless, colorless, thirst-quenching liquid found in lakes and running through our faucets.  Some of these standard beliefs may be false, but they still constitute the common wisdom which goes into what we ordinarily call the `meaning' of a term.  There is no such `meaning' to proper names.  A competent user of the name `Plato' needn't associate any standard shared descriptions with that name, and indeed need not associate any descriptions at all.  Proper names, in this sense, are indeed like pegs on which to hang descriptions (to use Searle's metaphor).  General terms, on the other hand, do come with standard stereotypes (the stereotype associated with a term `X' is the conventional ideas of what an X looks like, or acts like, or is).   The information contained in the stereotype sets the standard for semantic competence, though it isn't necessarily correct (it may be discovered that tigers are not actually striped, that the appearance of stripes is a result of some weird interaction of light with something in their skin).  The information contained in the stereotype is what is obligatory to convey when explaining the meaning of a term to a novice.  (Notice that there isn't really an analogue of `explaining the meaning' of a proper name, where you must go through a standard list of items.  To explain to someone how to use a name you can give whatever clues which would allow him/her to identify the bearer of the name.  Whereas to explain to someone how to use a term like `tiger' you must give a more or less fixed set of descriptions, roughly those that occur in the dictionary.)

Back to Twin-Earth
     Putnam concludes that we must recognize at least the following four ingredients in meaning:
(i) syntactic category to which the term belongs (noun, verb, ...);
(ii) semantic category to which the term belongs (natural kind term, event,...);
(iii) stereotype associated with the term (see above)
(iv) extension.

     The term `water' has the same syntactic and semantic categories and the same stereotype associated with it here and on Twin-Earth.  This means that we are the same as the Twin-Earthlings in point of semantic competence (regarding the word `water').  However, the extensions of our terms are different.  Their term applies correctly only to liquid with XYZ structure, our only to liquid with H2O structure.  If extension is included as part of the `meaning' of a term, then it trivially follows that meaning determines extension (you can't have two terms with same meaning and different extension).  But then meaning ain't in the head; it depends on extension, and extension is a matter of the structure of stuff in the world.  In any event, what's in the head (a person's psychological state - the set of the beliefs she associates with a given term) does not determine what terms in her language correctly apply to (what their extensions are).