conjunctiva
This is the thin layer of skin that covers the white part (the sclera) of the eyeball. The conjunctiva is very thin and has blood vessels coursing through it that you can see when looking in the mirror. The conjunctival skin also loops over and forms the inside of the eyelids themselves. This “looping” is what keeps objects like eyelashes and contact lenses from slipping completely behind the eye. When irritated, the conjunctival blood vessels dilate and make the eye look “pink.” This is called pink-eye, or more formally conjunctivitis. If a blood vessel breaks, blood can collect under the conjunctival skin and cause an impressive subconjunctival hemorrhage.