Simply......a LSD deliveres power to both wheels no matter their amount of friction on the ground.

Imagine you're rounding a hard left corner, and you step hard on the gas. Most of the weight is riding on the right rear tire, that wheel has a lot of friction with the ground. The left rear tire has very little friction with the ground, and starts to spin. with a "open" diff, most of the available power will be delivered to the left tire with little traction. On a LSD...the power will be delivered to both wheels much more evenly, thus the car can exit the corner faster as the power is pushing the car forward with the tire with good grip, not just spinning the tire with no grip.