Underarm hair, like pubic hair, is a secondary sexual characteritic.

it help establish your scent. Nowdays, especially in modern world, the idea of a personal scent is considered 'unattractive'.. but human still respond to them.

a study done with new mothers, had them smelling blankets..(used one night) most mothers could correctly identify which blanket their baby slept in. (it smelled the best!)

another study i read about, reported on small closed societies. (ie, amish). very often, a person found to smell unattractive, was also one who had too much of a genome in common..a bad genetic match.
(too much different also results in an unattractive smell-- a complaint often made about foriegners.. they smell bad)

so underarm hair (and the scent associated with it) becomes important geneticaly, once you reach puberty.. and it appears right on schedule!

the most common expression of this, is good old house hold laundry.. when your in love, you don't mind the smell of your loved ones laundry.. but fall out of love, and their clothes stink. secondly, most parents find the clothes of their teen age kids to stink-- a secondary protection against incest.