The idea that in the next 50 years we will hit the maximum oil production rate, and after that it's all downhill.  Calculations (guesses) about total oil resources vary from 1-2 trillion barrels.  That's a big difference if you consider that an extra trillion barrels would keep the world economy ticking over for another few decades.

Peak oil is about what you put in to the
tank of the car, climate change is about what comes out of the exhaust pipe.
People instinctively tend to be more concerned about what they're putting in
than what's coming out at the end, or at least see it more in the short term.  The concept of peak oil puts a mirror up to the community and say "where is this community's ability to withstand
shocks?" The climate change argument doesn't do that, it's a longer term
transition.

From Transition Culture