Introduction
The differential is the part of the car that translates the torque of the driveshaft to the rear axles. When a car negotiates a turn, the outside drive wheel travels a longer distance (rotating faster) than the inside drive wheel (rotating slower.) If the drive wheels are tied together they can’t rotate at different speeds which makes it particularly difficult to execute the turn as you get a combination of the outside wheel dragging and the inside wheel spinning. Ultimately this results in damage to the tires and difficult handling. In simplest terms, a differential allows the inside and outside wheels to rotate at different speeds while still being able to apply power.
There are a number of different basic differential designs. They broadly fit into the three categories of “Locked” or “Spool”, “Open” and “Limited Slip” differentials.

Locked or Spool
A locked differential is actually not a differential by design. It does not allow the two drive wheels to turn at different speeds. Its purpose is to ensure that both drive wheels turn at the same speed. It is used in some race cars and is most commonly found in drag and drift racing.
Open
A traditional open differential is the most common type found in cars today. It is a relatively simple mechanical design that typically consists of a set of four beveled gears that live within the differential carrier. Half shaft axles are connected to these for power delivery to the wheels.
The primary problem with a traditional open differential is that if a single wheel spins freely such as in ice conditions, or by the application of too much drive power, all of the power will be transmitted to the wheel that is spinning (path of least resistance). The other wheel which may have effective traction will get little or no power. This is particularly a problem on high performance and race cars which have the ability to break traction at will.
Limited Slip Differential
The goal of a Limited Slip Differential (LSD) is to allow some rotational difference of the two output shafts, but at the same time to limit the rotational difference. For example when applying power while exiting a turn, a car with a traditional open differential may spin one of the two tires slowing overall acceleration. When using a LSD, this unintended wheel-spin may be reduced or even stopped allowing the car to exit the corner faster. LSDs can also help under braking as well.
Usually LSDs have 3 adjustment settings that we can change. The number of clutch plates, the preload spring and the ramp angle on coast, throttle or both.
The number of clutch plates changes the amount of friction between the plates thus providing more lock. The preload spring sets the amount of force that is applied to the number of clutch plates. This means more preload = more lock. The ramp angle sets the amount of lock when off throttle and on throttle.
Below we can see what each setting change does to the handling of the car.
Note: In some cars the ramp angle settings might be reversed.