To clarify how a differential works: An open differential always divides TORQUE equally between sides. If the left tire slips due to lack of traction, the torque to the right side is limited to the level that the left broke traction at. At the extreme, say the left tire is off the ground. No torque required to turn a wheel that's off the ground, so the right side gets no torque, even though it may have traction on the ground, so you go nowhere.
The other end of the spectrum is a fully locking diff. such as a ARB or Detroit locker. This type can bias torque 100%. This means that in the same case of the left tire off the ground, the locker can bias 100% of the torque to the right. Meaning it can still apply torque to the limit of whichever tire has more traction.
A limited slip lies somewhere in between, some even tell you what the torque bias ratio is. If the ratio is, say, 2:1, then the differential can send 1/2 the torque that it took to break traction on the left side to the right side.
Brian