In particular, I suggest reading about the evaluation procedure: http://reference.wolfram.com/language/tutorial/EvaluationOfE...
In short, it's a term-rewriting language with a particularly complex (although carefully crafted) rewrite strategy. Rewriting and evaluation strategies have a rich base of history and literature to read up on too.
But really, the best way to get the flavor of Mathematica is to play with it. I recommend downloading a free trial, since the desktop application is much more responsive and interactive than the online version.
It's pretty fun and, once you get the hang of it, surprisingly useful. And I mean that both ways: 1) It's surprising how useful it is and 2) It's often surprising when it's useful. It was a pleasant surprise when I discovered how useful it can be and it's always pleasant when I'm surprised by an opportunity to use it.