Peak oil is the phenomenon of depleting oil reserves. The 'peak' is when production is at its maximum; after the peak it will go down and if this happens world wide, hell can break loose. The demand for oil will continue to rise for the next 40 years, mainly because of the economic growth of China, India, Russia and Brazil. Production will decrease, this automatically leads to increased prices (high demand + low production = high prices), even further fueled by speculation.
A lot of countries and areas already experienced a peak in production and are declining, see:
It is unknown when the worldwide peak will happen. Speculations are somewhere between 2010 and 2040. A slightly negative view of what could happen:
My own prediction is that the next 10 years will be okay, maybe oil prices now and then rising above 100-120 dollar per barrel, but no big deal. After that things will get worse. As I see it now, both politicians and most people don't want to spend too much money on wind/solar power or even nuclear plants. Only when oil prices will reach $150 or even $200 and remain above that for at least 3 years people will wake up. Then it will be too late though. Not only will electricity and car fuel become very expensive (expect at least 3x the current prices), but also ALL the products you buy in the supermarket or at any other store will become way more expensive. This is because the price of oil and therefore the price of fuels and electricity has a direct effect on ALL prices.
Governments all over the world will invest in wind power and/or nuclear, and eventually the demand for oil will decrease as well. Just in time before famine and anarchy will take place.
Summary of my prediction: