A pterygium is a growth that develops on the conjunctiva or mucous membrane that covers the white part of your eye. It is a benign or noncancerous growth that is often shaped like a wedge. In some cases, a pterygium can extend to the cornea. This is the clear part of your eye that covers your iris and pupil. Pterygium may be treated conservatively with medical therapy or removed with an in-office minor surgical procedure.