Axiom of Choice

I don't get the Axiom of Choice. All it seems to say is that if you have a bunch of piles of objects, it is possible to pick exactly one item from each pile. Well big fucking whoop, what's the big deal? Why is this so controversial?

Hmm... thanks, I kinda sorta get it now. (OP here) Basically, it's something that's so painfully obvious that you can't really prove it's true, and just have to assume it is (hence an axiom)- but in some cases you can get weird things to happen by assuming it's false. Right?