Most production cars have a wet sump oil system. The HowStuffWorks article on car engines shows you where the sump is -- it's the area below the crank shaft. In a wet sump, the oil that you put into the engine is stored beneath the crankshaft in the oil pan. This pan has to be large and deep enough to hold four to six quarts of oil -- think about two 3-liter bottles of soda and you can see that this storage area is pretty big.

In a wet sump, the oil pump sucks oil from the bottom of the oil pan through a tube, and then pumps it to the rest of the engine.

In a dry sump, extra oil is stored in a tank outside the engine rather than in the oil pan. There are at least two oil pumps in a dry sump -- one pulls oil from the sump and sends it to the tank, and the other takes oil from the tank and sends it to lubricate the engine. The minimum amount of oil possible remains in the engine.

Dry sump systems have several important advantages over wet sumps:

Because a dry sump does not need to have an oil pan big enough to hold the oil under the engine, the main mass of the engine can be placed lower in the vehicle. This helps lower the center of gravity and can also help aerodynamics (by allowing a lower hoodline).

The oil capacity of a dry sump can be as big as you want. The tank holding the oil can be placed anywhere on the vehicle.

In a wet sump, turning, braking and acceleration can cause the oil to pool on one side of the engine. This sloshing can dip the crankshaft into the oil as it turns or uncover the pump's pick-up tube.

Excess oil around the crankshaft in a wet sump can get on the shaft and cut horsepower. Some people claim improvements of as much as 15 horsepower by switching to a dry sump.
The disadvantage of the dry sump is the increased weight, complexity and cost from the extra pump and the tank -- but that's a small price to pay for such big benefits!