Headgear, headwear or headdress is the name given to any element of clothing which is worn on one's head.
Headgears serve a variety of purposes:

protection (against impact, cold, heat, rain and other precipitation, glare, sunburn, sunstroke, dust, contaminants, etc.)
to keep hair contained or tidy (including scrunchies, ball caps, etc.)
decoration or fashion
religious purposes
medical purposes - for example orthodontic headgear
modesty; social convention
distinction; a badge of office
sport uniform