LaTeX a bit like HTML or BBCode in that you will mix text and code that changes how your text is displayed. Of course LaTeX is way more powerful. (Actually, HTML+CSS+JS+MathJax comes close but is lacking when it comes to paged output and justified paragraphs.)
There are a number of reasons why people prefer LaTeX over word. Some geeks, I think, just don't like 'struggling' with WYIWYG (what-you-see-is-what-you-get) editors. They might feel they have more control over the output if they're writing code. The most cited reason, however, would be that it's too difficult to enter mathematics in word processors. This is relatively easy in LaTeX. A third reason is that it's just easier to get professional looking output using LaTeX. The way it decides where to hyphenate, for instance, is still superior to programs like Word (I've come to reckon the Word team does not consider this is an important feature).
LaTeX is the standard (source) document format in fields like mathematics, physics, computer science, and even parts of philosophy.
Although LaTeX is extremely powerful and is the only thing I use, I can't really recommend it unless you're sure you need it. Owing mostly to its old age it is a horrendously complicated system. Sure, there are nice abstractions for most things, but they're leaky abstractions, and the whole setup underneath is a mess despite impressive modernization efforts.
Thanks for that explanation, dove, appreciated. Yes, it sounds a bit above my league, both in terms of what I need but also what I can comfortably deal with technically. I'm based in the social sciences so what I'm working on are pretty much straight forward texts.