If you watch a cat blink, you will see a white membrane cross its eye – that is called its third eyelid. It is quite a rare thing in mammals, but common in birds, reptiles, and fish. Humans have a remnant (but non-working) third eyelid (you can see it in the picture above).
It has become quite small in humans, but some populations have more visible portions than others.
There is only one known species of primate that still has a functioning third eyelid, and that is the Calabar angwantibo (closely related to lorises) which lives in West Africa.