Various mammals, either when frightened or wanting to scare off another animal, display a reflex which makes the hair on their back and tail stand on end.  Animals are very good judges of relative size - and indeed numbers of potential opponents - and, unless trapped into doing so, are reluctant to attack if they don't feel they have a clear advantage.  So an animal making itself look bigger in this way brings with it a psychological advantage which might enable it to win the day and preclude an attack.

The hair of hedgehogs and porcupines has become sharp pointed quills and these animals when feeling threatened puff themselves up and turn to direct the sharp bits at their perceived attacker.

Birds don't have hair, but they do have feathers, and once again can make them stand on end if threatened or surprised so that they seem bigger and more dangerous than they really are.

We humans have no longer much hair to set on end, but we still do have the reflex and get goosebumps when spooked.