Your cat possesses one more eyelid (per eye) than you do. This is the haw eyelid, or nictitating membrane. (The verb nictitate means “to wink.”) The haw eyelid shuts horizontally (like a drapery being closed sideways across a window) instead of vertically (like a window shade drawn up and down), and is an extra layer of protection for the cat’s eye. Many other animals have them; humans don’t.