An open diff delivers equal torque to each wheel. When you go round a corner, the car experiences lateral load transfer, ie more of the car's weight is over the outside wheel than the inside. With an open diff, as the inside wheel goes unloaded (as less weight is going through it round the corner), the wheel has less grip.
A limited slip diff will transfer more torque to the wheel with more grip. Going round a corner, this means some torque is effectively taken away from the inside wheel and transferred to the outside wheel, which has more grip - the outside wheel will make better use of this torque as it is being pressed into the road harder than the inside wheel.
The result of this is more efficient delivery of power from the engine and transimssion, to the road.
In simplified real terms, if you're on a constant radius turn, ie a roundabout, as your speed increases your car with an open diff will be more inclined to understeer, ie you need to apply a larger steering input to maintain your heading as the car tries to go straight on.
With a limited slip diff (Q2) fitted, these understeer effects don't kick in until you're going much faster. This means that at a given speed, the car will grip much better with a Q2 than with a standard diff. The effects are far more pronounced in situations such as this, where the car is cornering fast. In 'normal' driving it won't have much of an effect - however when cornering fast you will be able to put much more power down (ie accelerate more) as the wheels will grip much more efficiently than with a standard diff.
Basically it makes it easier and safer to drive the car fast, as it won't lose grip until you're doing a much higher speed.
Fundamentally - it's amazing