Goosebumps are the result of small flexible muscles on the skin, causing the hair follicles to rise slightly. This causes the hair to stand up. Goosebumps are an uncontrolled reaction: sensors from the sensitive nervous system - nerves that control the fight or flight response - control these skin muscles.
In the animal kingdom, the threatened animal has a similar reaction, causing the fur to swell slightly. This makes the animal look bigger and more dangerous. Perhaps the most outstanding example is the hummingbird, which proudly shakes its head when exposed to danger. This can make a threatening enemy think twice before attacking. That may explain why the sensory system controls the goosebumps - the reflex is tied to a battle or flight response.