You "compile" papers into a camera-ready final form. It handles like page references, figure numbering, citations, etc. There's also a rich package system for extending features. Most people use it for its math typesetting features, which is now a fairly common way to write math expressions (mathjax, word's equation editor can understand latex, markdown). More fun, you can write your own macros and have some pretty rich commands and features.

Latex is very common in math and physics departments, and somewhat common in CS and ECE departments. It's still mostly for academic writing (papers and books), although because its plain-text and scriptable, its pretty nice for other types of documentation where you can bring in tons of things via a makefile.

LateX is very popular to write academic and scientific papers. It has a great support for mathematical formulas and every formatting option conceivable. I love it because it allows you to write papers using only your keyboard (no need for clicking 20 times to find the option in a menu). It's written as code, and then compiled into whatever format you'd like to use (pdf, etc)