Peak oil: the theory that given the fact that the supply of oil is limited, there is some roughly halfway point at which oil production peaks and subsequently declines. (Visualize the Bell curve: up, a peak or plateau, then down. Here's a diagram.)
This theory, as with all really good ones, was first laughed out of the room when presented in the 1950s by Shell geologist M. King Hubbert on US oil production. (By the way, he came up with his theory from observing the production of an individual oil well, extrapolated to an oil field, then further to the lower 48 states as a whole). His prediction that US oil production would peak in the 1970's turned out to be correct and now the theory is known as Hubbert's Peak.
People have now applied his formula to world oil production and are coming up with a time frame for peak oil of roughly 2000 (!) - 2015.
Some people confuse peak oil with oil depletion, the idea that we will run out of oil. Maybe some day, but long before we run out, oil supplies will get tight. That is peak oil. If the world is demanding 82 million barrels a day (a day!), and oil production starts to decline below that, obviously there's a bit of a problem.
One which, thankfully, capitalism will solve, though unfortunately not in the way we normally would hope. Rather than supply rising to meet demand, demand will have to fall to meet supply, and the adjustment will involve price.
So how do we tell if peak oil is here? Simple: Oil production will peak, plateau, then decline. Prices will rise, though probably be quite volatile as they go through "price discovery", trying to find the right balance between supply and demand. Which is to say, oil prices will trend up, but probably be all over the place.
Further reading on Hubbert's Peak and a prediction of a peak oil production date of Thanksgiving 2005 from Princeton professor Kenneth Deffeyes, who worked with Hubbert, here, and a recent presentation of his is available here. He also wrote a couple of good books on the subject, see sidebar.
An interesting paper on the topic here, maybe a little dated but still interesting.
Mainstream media has caught on too, with articles in National Geographic, Newsweek, CNN/Money, US News and World Report, and WSJ.