The way a standard open differential works is that the same amount of torque is applied to both drive wheels while the speed of the wheels is allowed to vary(This is needed because in turns the wheels spin at different speeds and if there was no differential things would get ugly). If one has less traction it will slip reducing the amount of torque required to spin the wheel.
Put it this way. One wheel is in the air and only takes X torque, lets say 20 foot lbs , to drive the wheel at some high speed (which does no work since it is spinning with no traction), and the other is in the mud where 20 foot pounds is not enough to move the truck out or get that wheel to slip.
Electronic limited slip uses a standard differential and the ABS system to apply the brake only to the wheel that is slipping to increase the torque required to spin it, which increases the torque to the wheel with traction until it can get you out of the mud. Get it. Other systems like Limited slip are different in operation but similar in result. There are styles that use clutches, gears, and dilatant fluids (Viscous).