Many animals have a third eyelid called a nictitating membrane. This clear eyelid can be drawn across the eyeball for protection from debris, prey, or the dryness of air, similarly to regular eyelids. Reptiles, birds, sharks, and some mammals evolved this extra layer of protection to keep their eyes moist and clean while maintaining visibility.
The nictitating membrane is part of the conjunctiva, a mucus membrane. Usually, it resides in the corner of the eye when not in use. In humans, this membrane is permanently folded into that corner; it's the visible pink nub. Most animals can control the haw, another name for the eyelid, by drawing it diagonally or horizontally across the cornea. When animals evolved to live out of the ocean, they had to develop a way to keep their eyeballs moist in dry air and free of particles in dusty wind. Predators, especially, cannot risk blinking their eyes repetitively, lest they miss a scurrying mouse or hopping frog. The nictitating membrane allows them full vision as well as the benefits of blinking.
The owl, like other birds, closes its haw when flying at high speeds because the additional moisture improves their vision. Certain kinds of sharks called carchariniformes, also use nictitating membranes to keep from being stabbed by thrashing prey. Amphibious creatures such as alligators, crocodiles, and other reptiles use their third eyelid while hunting, or while not underwater.
Harbor seals benefit from their nictitating membrane because they live in and out of the water. Aardvarks close their nictitating membrane when they are eating termites to keep from getting bitten. For the polar bear, the membrane actually filters ultraviolet light and reduces snow blindness. The nictitating membrane of other mammals, like cats, dogs, and horses, only protrudes if they are ill. A visible haw could be a symptom of dehydration, tetanus, low body weight, or an abscess near the eye.