Post-activation potentiation occurs only in fast twitch muscle fibers. It enhances muscle force at sub-maximal activation levels for a brief period of time following previous muscle activation. So let's say you are doing a set, then you rest long enough to reduce fatigue, the potentiation would be exhibited in the first few reps of the next set of a movement that has the same or close mechanical properties.
An experiment to see how this potentiation affects performance would be to do a couple heavy bench presses, then after a brief time (depending on how fatiguing the reps were) lay down and do a medicine ball throw, the power acheived should be much higher than if you just intitially tried the MB throw without the bench press reps. This is one of the reasons while you'll see jump squats height being higher after a brief set of squats. Again as long as the set isn't carried out too long.
Some of the potentitaion may actually be at the twitch level of the fibers, some of it may be an increased sensitivity to calcium. It's not really know as to why.
I personaly suspect it's a carryover from our days of having to quickly sprint away from something wanting us for dinner, then still having to jump up into a tree or similar events.
