It becomes important when you consider "days to cover". Just multiply the outstanding shares by the short float then divide that number by avg daily volume. That will give you an idea of how many days it would take short positions to cover at the given daily volume.
So if you end up with something like a 30% short float that would take 15 days to cover at current volume you have a situation ripe for a short squeeze. As if a binary event occurred that would create an above avg # of buyers pushing the price higher the shorts would be pressed into covering at higher prices pushing the price even higher.
The same thing can happen on the way down in a long squeeze but it's just not as notable as downside velocity is much more common.