Limited slip diffys help minimize wheel spin during low traction situations. If one wheel starts to spin (inner wheel in a corner, in the wet, etc) a clutching mechanism partially locks up the gears and transfers power to other axle.
For day to day driving, you won't notice an LS diffy much. For aggressive driving, it can help with power application in low traction situations.
It's not always your friend. For example, while an LSD can help you get started in the snow, it can also make a car more subseptible to swapping ends. An open diff will typically spin only one tire. The LSD will spin both causing a complete traction loss at the rear end of the car.
Bellevue WA
90 535iM - not much stock remains. 3.7 liters, ported head, cammed, 3.73 diffy, M5 brakes, MAFed, yadda yadda yadda
86 Porsche 951 - Track Toy