Peak Oil refers to the theory that oil production follows a bell curve, whether it is in reference to a specific oil field or global oil production.  On the upside of the curve, oil and its derivatives, are cheap and plentiful due to a high cost-benefit ratio (the amount of oil pumped is large relative to the amount of energy needed to actually get it).  At the top of the curve, something of a plateau (or peak) is reached, whereby oil output cannot be increased.  At the same time worldwide demand for energy increases.  This drives prices up.  On the downside of the curve, oil becomes increasingly scarce and correspondingly more expensive.  It simply takes more resources to get the oil out of the ground, reducing the cost-benefit ratio significantly to the point where that ratio becomes 1:1.  This means that it takes as much energy to get the oil as one would get from the oil it self... it breaks even.  

The ramifications of this could be immense and far-reaching for an energy-intensive world.  It could cause economic collapse as our economies are built upon growth (growth=energy, no energy=no growth).  The fallout from that kind of scenario could be catastrophic.  On the other hand, it may lead to a large scale retooling of our infrastructure to accommodate alternative energy sources such as solar, wind, ethanol, etc.   Opinions on how specifically Peak Oil will affect the world differ widely.

There are some who are steadfast in their belief that Peak Oil is a phenomenon that will have severe consequences for society at large.  Others view Peak Oil as a serious problem, but do not see it as a doomsday scenario.  And there are those who put no credence in Peak Oil theory whatsoever.  Peak Oil Resources will be party to all of those views, in one place, so that you can make a judgment call as to what may or may not be in our collective future.

There are a few great sites to start with that cover the spectrum of Peak Oil facts and opinions.  For very well done primers on the topic that address many different angles of the issue, see the following:

LifeAfterTheOilCrash - Hosted by Matt Savinar.  Fairly well researched and a great starting point.  

PeakOilDebunked - Do not be confused by the name.  The author believes that Peak Oil is a reality, but draws issue with some popular ramifications put forth by others.