How do pulleys works in a motor car?

They allow for a mechanical link from the engines crankshaft, to other components of the vehicle. (Via the drive belt)

They also allow for variable ratio's, to allow for items attached to the belt to turn at different speeds then that of your crankshaft.

Example:

Your crankshaft turns at 1000RPM,

Your alternator turns at 2000 RPM.

This is achieved by having a smaller pulley on your alternator then what is on your crank.

You can also have idler pulleys, and these merely provide a means to effectively route the drive belt.