Cured live rock: The term "cured" refers to the fact that it has all sorts of live things on it. It has sat in a store tank for a while, and it was piccked up all sorts of benifical bacteria, and it has no die off.
Uncured live rock: This rock is straight from the sea, to your door. There is more die off, and if you put it into your tank, it will start a cycle. It may be prefered if its a new tank. You get more hitchikers.