The ball bearings allow the weights to rotate without the bar in your hand needing to rotate. As you move a weight in most exercises, unless you have amazing form, some amount of rotational energy will be transfered to the weight. This is true in Olympic lifts even if you have perfect form.
If the weight was not allowed to move freely, you would need to counteract that rotational energy in order to keep your grip on the bar. So instead of the bar rotating in your hand, a bar with ball bearings allows the weight to move and the bar to remain still.