LaTeX is a system for preparing documents, an alternative to word processors like Microsoft Word. Many publishers use LaTeX for typesetting, but it is freely available and usable on many kinds of computers (i.e. you don't have to be a corporation to use it).
LaTeX is primarily meant for printed media (articles on paper), but can also produce slide presentations (a la Microsoft Powerpoint), letters, crossword puzzles and much more.
LaTeX is free. LaTeX is free as in price, and free as in freedom. You can download and install it free of charge, and install it on as many computers as you want and share it with your friends.
LaTeX is pronounced "Lah tech."
Processing this text produces this document (PDF).
\documentclass{article}
\title{An example of \LaTeX{}}
\author{Joel J. Adamson}
\date{\today}
\begin{document}
\maketitle
\tableofcontents{}
\section{Introduction}
This is the Introduction. Allow me to introduce \LaTeX{} to you.
\section{Next Section}
This is a section. Sections are important for specifying the
structure of your document. Think of your structure as an outline.
\subsection{A Subsection}
Another important piece of structure is the subsection.
\subsection{A Subsection with Equations}
Here's an equation:
\begin{equation}
\label{eq:1}
E = mc^2
\end{equation}
And another!
\begin{equation}
\label{eq:2}
L_1 = \sum_i (y_i - \alpha - \beta x_i)^2
\end{equation}
That's the end.
\end{document}