The nictitating membrane is a transparent or translucent third eyelid present in some animals that can be drawn across the eye for protection and to moisten it while maintaining visibility.

What purpose does a nictitating membrane serve?

“A nictitating membrane is found in many mammals, although we humans have lost it,” says zoologist Sue Evans at University College London. “Its main function is to clean and wipe the surface of the eye. In frogs it is basically a modified part of the lower eyelid, and thus modified skin.”

Why do humans not have a third eyelid?

It's vestigial, meaning it no longer serves its original purpose. There are several other vestigial structures like the plica semilunaris in the human body. Most of these became vestigial long before homo sapiens existed, quietly riding along from one of our ancestor species to the next.