The Cornea is the clear part of the eye that covers your pupil and iris and is curved like a dome. It bends light into your eye so you can see clearly. There are a number of conditions involving the cornea that would require the advice and care of an ophthalmologist (eye doctor).
Here are some pages detailing the various conditions regarding the cornea:
Corneal Abrasions
Corneal Laceration
Corneal Erosion
Corneal Dystrophies
Corneal Transplants