It's a branch of Philosophy, and you prove truth and validity of arguments using symbols... And logic.
I don't even know how else to describe it from there. It's rather complicated unless you know all of the vocabulary! I take it as a quantification requirement, because I hate algebra-type classes. It's actually very interesting and challenging, in a good way, but these past few weeks/sections have been brutal. But, it's still a better choice for someone who is more geometrically-minded (like me) than algebraically.