Your coif is your hairstyle. If you want to protect your coif in the rain, don't forget to bring your umbrella!
In the United States, coif is short for coiffure, which means "fancy hairdo." If you've arranged your hair into complicated braids anchored by bobby pins, go ahead and call it a coif. This word can also be used as a verb. If you're going to a black-tie event, you might want to coif your hair in an elaborate and elegant way.