Latex is a document preparation system

You use Latex to create documents for others to read. In that respect it is similar to Microsoft Word. But the similarities end there.

Document preparation with Latex typically consists of using a text editor (such as Emacs, vi, or even Notepad) to edit a Latex source file, which has the extension .tex, and then running the latex program to convert the source file to a document interchange format such as Postscript or PDF. Once the document is in a document interchange format, it can be previewed on the screen, sent to others, printed, etc.

What is up with the name "Latex"?

The name is (in my opinion) the worst part. It is too easily confused with latex, a synthetic rubber-like substance, and it seems elitist to many people. But try to forgive the name; it was created by Computer Scientists like me, and we're terrible at naming things.

Pronounciation: I usually pronounce it "LAY-tek", though some pronounce it "LAH-tek". In any case, the second syllable is not pronounced "teks".

Typography: In an obnoxious combination of captialization, font sizing, and baseline offsetting, Latex is often (and officially) written L^AT_EX. Actually, the HTML doesn't really do it justice, so I made the following image using Latex itself:

Even by writing "Latex" instead of "LaTeX" or "L^AT_EX" I'm violating the "recommended practice". But the other forms are just too annoying. The reason for this bizarre arrangement of letters is in part to distinguish it from the aforementioned rubber-like substance, but mostly to show off what is possible in Latex (encouraging the perception of elitism).

Etymology (word origin): Donald Knuth created "Tex" ("T_EX"), the three letters actually being uppercase Greek tau, epsilon and chi. This Greek "tex" is the root of English words like "technical" and "technique". Later, Leslie Lamport built "Latex" on top of Tex, prepending the "La" presumably to reflect his name.

Markup versus WYSIWYG

To someone familiar with MS Word or the like, the most radical aspect of Latex is that you do not (necessarily) interact with a graphical user interface (GUI), and you do not immediately see how your document will be typeset.

Consider a typical WYSIWYG ("what you see is what you get") word processor, such as Open Office, shown in the screenshot below:

In such a program, the GUI always shows what the final printed copy will look like, including formatting, etc. The GUI further contains a bunch of buttons (etc.) that can be used to apply formatting.

In contrast, the usual mode of interaction with Latex is via a text editor. The screenshot below shows fox.tex being edited in Emacs:

Here, we just see the plain text input file, plus the markup commands that apply formatting. This is similar to HTML. Actually, Emacs does show a little more than the plain text, by using different colors for different elements of the Latex input file, and even using boldface for the text that follows the boldface markup command "\bf".

When you want to see how the document will actually look when printed, you invoke the latex program to generate (typically) Postscript, and then view that with a previewer program such as gv. Below is a screenshot of using gv to look at the output of fox.tex:

Postscript is a good interchange format on Unix systems, but in the Windows world, PDF is much better. I usually convert Postscript to PDF using ps2pdf. You can also use a specialized version of latex called pdfTeX. The produces output that works better with onscreen previewers; they should produce identical printed output. Both are typically included with Latex distributions.

What is good about Latex?

Why would anyone use Latex? Here are some good points:

Superior typographic quality. The main reason I use Latex is it produces output that is, typographically, far better than any of the alternatives. Latex has excellent built-in fonts, good algorithms for automatic spacing, and the ability to fine-tune the spacing arbitrarily. Bad typography gives a bad first impression, and reflects poorly on the content of a document.
Output device independence. MS Word has (what I consider to be) a bug, where the formatting applied to a document depends on the printer designated as "current". Latex has no such misfeatures.
Compatibility with revision control. Because .tex files are plain text, I can use revision control software to remember the history of changes. Off-the-shelf revision control software has features that far exceed MS Word's built-in history mechanism.
Portability. Latex runs on virtually any operating system in existence. MS Word only works on Windows, and even OpenOffice does not run on all Unixes (though that is improving).
Document longevity. Latex documents written 10 years ago still work and still produce the same output as they did when originally written. In contrast, Microsoft uses version evolution as a strategic tool to force people to upgrade continuously, so MS Word documents are typically useful only for 3-4 years.
Macros and other programmatic features. Latex lets me define macros, canned sequences of text and/or markup, that I can then use repeatedly. It's much better than copy+paste since it can be changed by changing just the definition. Even more, Latex allows people to write programs in their documents, which is handy on occasion (mostly for people who already know how to write computer programs).
Mathematical typesetting. Typesetting mathematics is why Tex was first created, and Latex continues to excel at this task.

What is bad about Latex?

So why would anyone not use Latex?

More moving parts. Using Latex means using an editor, latex itself, a document previewer (such as gv), and usually a few other assorted programs. In contrast, WYSIWYG word processors are self-contained.
Difficulty knowing/remembering markup commands. Learning the markup commands takes time, and it can initially be quite frustrating. That is why I recommend the use of a front-end GUI at first; see below.
Previewing delay. There is a delay between typing something in the editor and seeing the result in the document previewer.
Possibility of syntax errors. Unlike in a WYSIWYG word processor, it is possible to create a .tex file that latex will reject, complaining of a syntax error. Worse, the actual error report is needlessly cryptic. It takes a bit of experience to learn how to deal with these errors.
Adding new fonts. You can't just download some .ttf (TrueType Font) file off the web and start using it. In fact, I don't even know how to add a new font (though I'm sure Google does). Whatever the procedure, it's not trivial.
Lack of support for newspaper-style continued columns. Newspapers often have articles that span multiple columns, on multiple (possibly disjoint) pages, in ad-hoc ways. Further, a single physical column may contain text from several articles. Latex does not support such complex page designs. (Of course, neither does MS Word; this is a comparison to the Framemaker class of desktop publishing software.)

How do I get started?

If you want to get started using Latex, here is what I recommend: