Peak Oil is the idea that someday soon (or perhaps already) humans will have taken out more oil per day out of the ground then we will ever be able to take out again. If you read over the site Matthew Savinar presents his case that this event will happen soon. He also details his vision for what this means for America and the world economy. I think that he presents a compelling case, but I'm not qualified to assess his interpretation of the facts. I tend to be impressed by the sense that the oil companies have begun to act like this is going to be true.
The biggest effect that this would have on our way of life is that decisions about energy would be made on a much different basis. I have started to take this into consideration when I make decisions that will affect my life. I make my decisions based on the assumption that at sometime in the next 5 to 10 years oil will cost anywhere from 2 to 5 times what it does now. There would also be corresponding rises in the costs of natural gas and electricity. Fuel economy and conservation become much more important factors in purchasing and using anything that consumes energy.
This whole subject is something that I am still pondering at times, I'm considering other points of view, but I must say that it has had an effect on the way that I make decisions.