A differential is a device, usually consisting of gears, for allowing each of the driving wheels to rotate at different speeds, while supplying equal torque to each of them.
A vehicle's wheels rotate at different speeds, especially when turning corners. The differential is designed to drive a pair of wheels with equal force, while allowing them to rotate at different speeds.
Power is supplied from the engine via the gearbox to a driveshaft which runs to the rear axle. A pinion gear at the end of the propeller shaft is encased within the differential itself, and it engages with the large ring gear. The ring gear is attached to a carrier, which holds a set of small planetary gears. The three planetary gears are set up in such a way that the two outer gears can rotate in opposite directions relative to each other. The pair of side gears drive the axle shafts to each of the wheels. The entire carrier rotates in the same direction as the ring gear, but within that motion, the side gears can counter-rotate relative to each other.
Limited Slip Differential (LSD)
A limited slip differential has all of the same components as an open differential, but it adds a spring pack and a set of clutches. Some of these have a cone clutch that is just like the synchronizers in a manual transmission. The spring pack pushes the side gears against the clutches, which are attached to the cage. Both side gears spin with the cage when both wheels are moving at the same speed, and the clutches aren't really needed -- the only time the clutches step in is when something happens to make one wheel spin faster than the other, as in a turn. The clutches fight this behavior, wanting both wheels to go the same speed. If one wheel wants to spin faster than the other, it must first overpower the clutch. The stiffness of the springs combined with the friction of the clutch determine how much torque it takes to overpower it.
A Viscous Coupling replaces the differential entirely. It works on the principle of allowing the two output shafts to counter-rotate relative to each other within a viscous fluid. The fluid allows slow relative movements of the shafts, such as those caused by cornering, but will strongly resist high-speed movements, such as those caused by a single wheel spinning.
A relatively new technology is the electronically-controlled active differential. A computer uses inputs from multiple sensors, including yaw rate, steering angle, and lateral acceleration and adjusts the distribution of torque to compensate for undesirable handling behaviors.