What is LaTEX

LaTeX is a software package for creating documents: anything from simple letters and memos to technical manuals, technical publications, overhead slides for seminars, to complete academic dissertations.

Advantages include:

It is robust (i.e. does not crash!)
It is available for many types of computer (Windows, Unix/Linux, Macintosh)
The source files (.tex files) are very small - not much larger than the raw text of a document itself.
It takes care of formatting for you using style files.
It is completely free.
Once you've mastered it via some examples, it is very easy to use.
Many people have contributed extensions to it for specific purposes. For example, style files for typesetting a resume.
The documents you create are portable from one machine to another.
It does an excellent job of typesetting mathematical formulae.
It can work at high resolution (600DPI) for high-quality printing.
It is stable - you don't need to upgrade your software all the time.
It is (essentially) unchanging: documents created will always be able to be edited and printed, even if created some time ago.
A companion program called bibtex can format references automatically for you, in many different formats.
Complex tasks, like creating a table of contents, are very easy. You just type \tableofcontents and LaTeX does the rest for you.

The disadvantages are:

It can take a while to set up on your computer. (These pages should have all the necessary links to what you have to download)
It takes a bit of getting used to.
The error messages it generates can be rather cryptic.

For interest, here are some examples of LaTeX/TeX formatting of professional documents.
Warning: these are very large documents.