Goosebumps (or goose bumps) is the common name given to the
archaic reflex response known as Piloerection. This
reflex is a
throwback to a time when our hairy progenitors warmed themselves by activating tiny muscles in the skin, called arrector pili. These muscles tugged on
hair follicles, puckering up the skin around those follicles and fluffing up the fur so that warm air got trapped near the skin.
Piloerection also occurs during intense fear; this puffed up your ancestors' hair to make them look larger and more fierce.
According to
melknia, piloerection also occurs when some rodents—like rats, mice and bunnies—are ill.