The secret to quattro lies in the center differential as pcholakov details above. These days it is implemented in one of two ways depending on engine configuration. Those cars which have a longitudinal engine configuration use a Torsen differential. Those with a transverse engine configuration use a Haldex clutch.
quattro systems with the Torsen differential have two EDL (electric differential lock) open differentials, one at the front and rear, and are known as quattro IV. quattro systems with the Haldex clutch have two EDL open differentials, however the default duty of the Haldex clutch is to provide no power to the rear wheels. When the front wheels begin to slip, the Haldex clutch will engage the rear wheels to compensate.
The Haldex system is found in Audi TTs, S3s and A3s, and also in the VW 4Motion Jetta and Golf.
You may hear people talking about full time quattro, in which case they're talking about the quattro IV system.