Disclaimer: I work with an older 202 straight 6 Holden engine in a landrover, so my perspective is somewhat vintage. However the basic underlying concepts are the same.
Cause: Low oil in the oil pan, at the very bottom of the engine. Normally the oil should read right on the Full line on a dipstick, when the vehicle is level and the motor is cold and has not run for several hours. This allows the oil in the upper part of the engine to run back down into the pan.
Explanation: The oil is drawn from the pan into a pipe called the oil pickup. This is a hard pipe that hangs down into the lower part of your oil pan. As long as this part is covered by oil all the time, you're good. On a steep ascent or descent, the oil may move away from the pickup, which is the same condition as when there's low oil all the time. Also, hard cornering can slosh around the oil so the pickup comes clear for an instant.
Here's an oil pickup and screen in place. The pan is not there, and this motor is upside-down.
If the pickup is uncovered, it will attempt to suck in crankcase air rather than straight oil. Since air is far more compressible than oil, the effective oil pressure drops with air in the line. The oil pump should push through most air bubbles, but in the worst case it may end up empty of oil, and filled with air instead. This could cause an air lock and oil simply stops flowing.
Effect: Your motor pumps the oil up the side of the engine into the head, where there are lots of moving parts like cams and cam followers. My motor has push rods and rockers and valve stems that all need to be lubricated continuously. With a lower oil pressure from the pump, less oil gets pushed to the top of the engine and these moving parts can run drier.
In addition, there are oil throwers and slingers at various places around the main crankshaft. These catch and scoop oil and throw it into/onto places that need lube, like the cylinder walls when the piston is up, and into the connecting rod eye bearings. Should the oil level drop low, this lower-engine lubrication is reduced, and things run hot, with increased friction and wear.
I recall that the average car engine cycles its entire store of oil through the engine 4 times a minute. I suspect its more often in a more recent engine.
Source - this is worth watching: http://www.youtube.com/watch?v=CDXXkpGiLU0
Its not all bad - there are more modern systems like dry sumps in racing cars, where the oil is pumped into a holding tank under pressure and then fed to the engine, so its got a reservoir of oil for the corners. You still shouldn't run out, but you can hard-corner without loosing lubrication.
Story: My other-half's car was sounding very tappity, but otherwise ran okay. Wasn't till she was driving the car up a decent grade that the oil pressure light came on. It was 2 litres low, and barely registering on the dipstick at all. A couple days later, she drove the car out of the garage and then checked the oil. It read real low because the motor had just been running. So she put an extra 2L in and drove for 30 minutes. Car was running really badly, blowing blue smoke as the oil was forced around the rings past the pistons and into the combustion chamber. We drained some out and all was well.
So its a case of too much is bad, not enough is bad, and just right is just right.