In a corner, the outside wheels need to go a wider distance than the inner wheels. To enable this, cars use a differential, which allows power to be sent to both wheels while they're turning at different speeds. If both wheels were locked together, both wheels would try to stay at the same speed and therefore resist going into a corner. This means understeer (the car will push). A limited slip differential allows to dial in any value between an open diff (0) and a locked diff (100).
Higher amount of lock => more UNDERSTEER.
Now why would you want that? Basically you don't, but there's a problem with an open diff. If you've ever tried turning a drive wheel of a car on a lift, you'll have noticed that the opposite wheel starts to turn in the opposite direction. This means one wheel needs to support the torque of the other wheel. If one wheel can't transmit any torque, e.g. because it's standing on a patch of ice, the other one can't either, even if it's sitting on grippy tarmac. If you now try to accelerate, the grippy wheel will just sit still, while all the power you apply will be used to spin the tire on ice. The same happens to a lesser degree during cornering. Weight shifts from the inner to the outer tire, so the inner tire can transmit less torque. If you reach the limit of what the inner tire can put on the ground, it will start to slip and any excess power is going up in smoke at the inner wheel. Locking the diff will send more torque to the outer wheel, so the power the inner wheel can't transmit will be used for acceleration instead of smoke.
So LSD => more traction, more understeer.
Up to a point, that is, and here we come to the drift car. Because now you can transmit more power to the outer wheel, this means also that you can break traction at the outer wheel much easier. So if you have enough power to spin both rear wheels, things will snap into power oversteer.
So why are there three settings?
Most common LSDs use clutches to resist one side of the diff spinning faster than the other. The pressure on the clutches depends on the amount of drive torque. So if there's no torque, the diff behaves like it's open, under load it starts to lock.
The "acceleration" value determines how much the diff locks under power (as described above).
The "deceleration" value comes into play under engine braking, i.e. when you get off the throttle. Again, a higher value gives you more understeer, so you can make the car more (and also too) stable when you lift off (Porsches e.g. often even use higher values on deceleration than acceleration, to prevent exiting the corner ass first).
The "initial" value is the preload on the clutches, so it determines how much the diff is locked all the time, even without torque applied. This will make the car feel more stable overall, but again also means understeer.
