One evolutionary explanation for the fine hair, known as vellus, could be to protect us from parasites. Researchers placed bed bugs on a shaved patch of arm to test against the unshaven arms of volunteer students:

Turns out students were significantly more likely to sense bedbugs crawling on their unshaven arms. And those tangles of hair slowed down the bug's search for a place to snack, too. The authors say our fine human hair may thus be perfectly evolved: thin enough to eliminate hiding spots for bugs, but thick enough to act as an alarm system for bloodsuckers in the night—enough to make anyone's hair stand on end.

(Photo by Armed Forces Pest Management Board)