Is there any biological importance to human hair?

Hair on some parts of your body is there for a reason:
Eye-lashes and eyebrows help to protect your eyes (believe it or not, eyebrows actually have a function for more than being raised whenever someone says something stupid).
Hairs in your nose and ears are intended to prevent foreign matter from getting in and causing damage.
Hair in the groin and armpits has a very old biological function that helps to regulate the temperature of certain glands and to collect scent to "attract" a mate (although most people now associate this smell with being dirty rather than with hormonal and chemical attraction).
The tiny hairs all over your body are intended to help regulate body temperature (although there are so few of them that it hardly makes a difference in this regard), increase sensitvity (you'll notice that if you shave your legs they will lose sensitivity to light touches) and to give extra protection from minor abrasions.
Men's beards are apparently a primordial symbol of masculinity that is used to attract a mate and to dominate other males (much like a lion's mane), but socially there no longer have this function.
As for the hair on your head... I have absolutely no idea.
Kal