A cat's third eyelid - sometimes known as the haw - is on the inside corner of
the cat's eye. This is the nictitating (or blinking) membrane, which helps
to protect the cat's eyes. If the cat is in too much bright light, the
nictitating membrane partially covers the eye to filter the dazzle. It also
serves to clean the surface of the eye, and protects from dust and dirt.
Sometimes a small piece of grit may enter and get trapped under it and may
require surgical removal - complete with anesthetic. Be sure to consult your
vet if you see your cat's eye weeping, or if you see him pawing at his face,
or if you can see only one nictitating membrane.
In some cases, the haw only becomes visible when your cat has a virus, is
debilitated, or is recuperating from an illness. In such cases, the fat
stored around the eyes which help cushion them from blows, is broken down to provide essential energy for your cat. The eyes will sink back and become partially covered by the nictitating membrane.
This all can look so alarming to you, I know, but remember that it is a
useful warning sign of illness, and will alert you to seek your vet's care,
especially if it remains visible for more than a day or two.
-- Unknown