Uncured live rock has is live rock that was collected in the ocean, and then shipped in damp paper (or similar) to your LFS, during wich time a lot of the life on the rock will die off. Whe it gets into your tank, all the dead stuff will rott in your tank, causing an amonia spike wich causes more life on the rock (and any fish/inverts you introduced previously) to die off - the procces continues itself until bacteria grow and take care of the amonia, by turning i tinto nitrite, then a second type of bacteria develops and turns nitrite into nitrate.
For cured live rock, the procces has already been done, although this rock won't be completely cured when you get it unless the curing procces happens locally (becuase the rock still gets shipped in wet paper where it will dry out a bit and stuff will die off). I'm pretty sure precured live rock is the same thing.