Sometimes a wheel on one side of a vehicle needs to spin faster than the wheel on the other side. While some wheels may spin freely (due to not being attached to an axle), wheels that are driven by the engine need to be on an axle, and this axle needs to allow the wheels to spin at different speeds; the differential allows this to happen. Two axle-mounted gears spin against each other by means of two other gears. The non-axle-mounted gears are attached to an assembly which is turned by the engine power.
Limited-Slip Differentials by Engineering Explained
A differential on its own would natually send power to whichever wheel is the easiest to send power to, which would always be the tire in a low traction situation. In order to avoid this, a limited slip differential resists having the two outputs rotate at different speeds.
Viscous Limited Slip Differentials by Engineering Explained
In a viscous limited slip differential, fluid is used to resist slip between the left and right wheels.
Torsen Limited Slip Differential
Torsen differentials use a special gearing design to reduce speed differences between wheels.
Hunting Gears by Cars Simplified
Hunting gears have teeth that "hunt" for the starting point and come across every tooth once before arriving at the starting tooth again. This approach keeps noise down and durability high. Most modern differentials have hunting gear final drive ratios.