What is the medical term meaning goosebumps?

Piloerection
Cutis anserina. It's actually body hairs which involuntarily develop 'rises' or bumps after someone has experienced a strong emotion or a cold sensation.

Oddly enough, goose bumps are the defense mechanism for porcupines and hedgehogs, in which they raise their quills to avert confrontation. That's an automatic reflex.

Cool!
horripilation