Your engine creates rotational energy. Co-ordinating explosions of gasoline to spin a metal shaft (the crankshaft), your differential performs the important job of helping to transmit that energy to your wheels, but in a very special way.
Imagine you have a barbell with weights on each side. If the weights were glued or welded to the bar, and you had to rotate it. If the weights cannot rotate independently of the bar, the only way to do so is to drag the weights along the floor.