The differential allows an axle to split the power between two wheels. It also allows for one wheel to spin faster or slower than the other without binding. That may sound odd, but every time you make a turn in your Jeep, the outside wheels need to travel slightly farther than the inside wheels. Without a differential, you would only be able to drive your Jeep in a straight line.
In addition to a tradition open style differential, there are also locking differentials that allow you to override the normal function of the differential and permanently lock the two axle shaft halves together. This is especially useful offroad for maximum traction.