A feature of the skulls of most Prosimians (including humans). It is formed by a downward extension of the frontal bone and an upward extension of the zygomatic bone, forming an extended 'bar' which supports and protects the eye.

Have you ever tried to find the eye socket on a dinosaur skeleton? All they have are these giant weird-shaped holes covering half the skull. Well, in primates that hole has been sliced in half by the postorbital bar, making a neat round circle for the eye to peak out of. (The brain case has also expanded, shrinking 'the other part of the hole' down to almost nothing).

And the reason? Because our ancestors leaped about in the treetops. For this, they needed steady eyesight (and stereoscopic vision, which is why our eyes are on the front of our heads). Many animals have their jaw muscles running right along side of their eye muscles. When the jaw muscles move, so do their eyes. This could be fatal in a tree dwelling animal. So first our ancestors got the postorbital bars, and then they encased their eye sockets entirely in pockets of bone.

A smart noder might try to jump ahead here, and postulate that other animals, like birds, would also need postorbital bars. Well, some other animals do. Cats, for example, have partial postorbital bars (the points don't quite meet over the eyeball), in order to aid them in their pouncing on small animals. But not birds. Birds took the easy rout, and simply fixed their eyeballs immovably in their skulls (no eye muscles).

Horses, cows, and many other ungulates also have postorbital bones, but for a completely different reason. They need strong jaw muscles for chewing up tough grasses, and the postorbital bar gives those muscles more support.