Cycling glasses can be found on many cyclists, for good reason. They serve as much in function as they do for fashion. We'll outline some of the functional aspects here; fashion is purely up to you.
Protection for your eyes
Cycling eyewear's primary function is to protect the eyes both from impact with road/trail debris and from the sun. They are generally impact resistant and made of quite sturdy plastic in order to defend your eyes against things like pebbles, sand, sticks, or anything else your tire or the tire in front of you kicks up. Cycling glasses also help keep water out of your eyes in the rain and bugs out when those little buggers are everywhere.
For protection from the sun, there are different shades of lenses that you can choose from to tailor the level of light being emitted to your eye. Some lenses are photochromic so that they darken as more UV light hits the lens, giving them a range of light filtration within the one lens.