Peak Oil, also known as the Hubbert Peak theory, Is simply the concept that at some point the amount of oil that we can pump from the ground will "peak" and supplies will then start dropping as known sources are depleted. That is it.
Many people, with a variety of ideas about where this will lead civilization have latched on to the Peak Oil banner, and have tried to attach their own theories. These range from the collapse of civilization, to the ways to make money off the coming price increases. Not to mention, all the predictions of when this will happen, and how fast it will have a disasterous effect.
There is also the battle about whether the source of oil is biogenic or abiogenic. This part of the argument is extra funny because the biggest Peak Oil loonies seem to think that it has some sort of bearing on whether we will actually reach such a state. It doesn't amke a damn bit of difference. Peak Oil will happen either way.
I've been following Peak Oil discussions, and ththis section is where you will be able to find all my rants about the idiocy on all sides of the debate.
For more information check out the wikipedia Peak Oil entry.