If the pterygium is removed and an autograft is not placed, then there is a high risk of the pterygium returning. The conjunctiva surrounding the pterygium has also been damaged by the sun, and there is a risk that the pterygium can return larger after the procedure. Using a conjunctival graft greatly reduces this risk.
A small piece of conjunctiva from under the eyelid is transplanted to replace the pterygium. (The conjunctiva under the eyelid has not been exposed to the sun and rarely turns into a pterygium.)
Because this tissue comes from you, it is called an autograft, and there is no chance that the graft will be rejected by the body.