The differential helps distribute power from the transmission to the driven axle, and it also allows the wheels to operate independently from one another. This comes in handy when turning, driving on slippery road surfaces and off-roading, as each wheel can get the amount of torque it needs to spin properly, even if they all need different amounts.
However, an open differential cannot divvy up the torque on its own. In many vehicles with all-wheel drive, the differential must rely on limited slip differential (LSD), or positraction, to allow for varied distribution of torque. There are a number of different limited slip differential systems, including Torsen and locking differentials, viscous couplings and clutch-type LSDs.
Clutch-type LSDs are the most commonly used version. They're built just like open differentials, but they also include spring packs and a set of clutches. The clutches are used to make one wheel spin faster on a turn, and they do so by fighting a wheel's attempt to spin faster than it should. Half are used with the drive shaft, and the other half are coupled with the differential's ring gear.
An LSD comes in handy if, for example, your car is stuck on an icy patch. If one wheel is on the pavement and the other is on the ice, an open differential will only provide enough torque to spin the wheel resting on ice without slipping. The other wheel will not have enough torque to move the car. The LSD allows the pavement-wheel to get more torque from the engine without delivering more to the wheel on ice.
If you're wondering whether your car has an LSD or an open differential, you can jack up the driven axle and spin one of the wheels. If the other one spins in the same direction, your car has an LSD. If it spins opposite of the first wheel, the vehicle is equipped with a standard open differential.