What is LaTeX?

The LaTeX Companion by Goosens, Mittelbach und Smarin explains LaTeX in the introduction as follows:
"LaTeX is a generic typesetting system that uses TeX as its formatting engine."
Although this sentence may not make very much sense on first reading it gives us a valuable information: LaTeX is not a wordprocessor but a typesetting system that achieves beautifully typeset documents without any deeper typographic knowlede.

Where does LaTeX come from?To better understand LaTeX we'll take a closer look at the origins of this software. In 1977 Donald Knuth began developing the typesetting software TeX. TeX (say: Tech) consists of the greek letters Tau Epsilon Chi and stands for virtuosity and applied knowledge. Knuths target group were mainly scientists who wanted to have influence on how their publications would appear on paper. Even though it was somewhat complicated to use, TeX established itself due to very flexible features to typeset equations. TeX became a standard for engineers and natural scientists alike.
Based on TeX Leslie Lamport created LaTeX during the 1980s, which made using TeX a lot easier. Users did not have to know hundreds of commands, but could create complex documents with only a handful. Meanwhile TeX is very widely-used in form of LaTeX. Contrary to TeX it is sufficient in LaTeX to mark the logical structure of a document, e.g. headlines, captions, footnotes etc. The compiler automatically translates this structure into TeX command. By default TeXShop will output LaTeX as pdf, so that printing and sharing a document are no problem at all.

How does LaTeX work? Typical wordprocessors like Word and AppleWorks follow the WYSIWYG-principle (What You See Is What You Get, or how you see it on the screen will also be how you'll see it on the paper), but often don't really comply with that. Working with them requires you to mark a certain area of text and then apply certain properties. You could mark a specific word, go to the formatting menu and select bold in order for the word to be printed in bold type.
LaTeX documents can be compared to HTML documents using a mark-up language. In order to print a word in bold type you'll need to add a command to the text. It could look like this:

This word should be \textbf{bold}.
And, when printed, would look like this:

This word should be bold.

A simple document

A simple document could look like this:	On paper it could look like this:
`\documentclass{article} \usepackage{english} \begin{document} \section{This is the title} This is the text. \end{document}`	1 This is the titleThis is the text.

By examining this example you can understand how LaTeX works. Commands are always added to the text by putting a backslash in front of it (\). In the preamble global properties will be set for the whole document, such as the document type. This example uses the "article" class as a "template". There are several more classes such as "report", "book" or "letter". Others, especially made for specific needs such as German or French conventions can be downloaded via the internet. The command usepackage{english} tells LaTeX to use English hyphenation for the whole text.
The main text will be placed between begin{document} and end{document}. Commands affecting the formatting or structure can also be added here. Using section a new section with the headline "This is the title" is created. With just one more command you can add a complete table of contents for your document, which is a real pain in the neck with most current wordprocessors.
By utilizing certain classes and styles all kinds of documents from novels to advisery opinions can be created. LaTeX documents can be used on all computer systems without any compatibility issues. Since it brings it's own fonts you will not be surprised by randomly substituted fonts on a different computer, as other programs do.
Granted, LaTeX documents may look very confusing at the first glance, but if you take a closer look you'll notice how structured and comprehensible they are.