Know anyone with two different colored eyes?
The condition is called heterochromia. Eye color, like hair and skin color, is a result of melanin. Thus, when the eyes of an individual are different colors, the reason almost certainly has something to do with that person's melanocytes, the cells that manufacture pigment.
Lots of pigment makes eyes brown, some pigment makes eyes green, and little to no pigment makes eyes blue. Most often, heterochromia is a result of some mishap in the life of one's melanocytes, resulting in a blue eye not exhibiting the pigment of its darker-colored partner.
What can go wrong with melanocytes? They can get lost. Most of the melanocytes in our bodies are produced in one location in utero and have to journey to their individual destinations. To get to where they belong, other cells have to send them the proper signals.
A number of things can go wrong. One example is Waardenburg syndrome, where genetic mutation results in wayward melanocytes that never find their way to the iris for which they were intended. In some cases, only some of an eye's melanocytes get lost, resulting in patches of different colors in the same eye.
Or nothing at all may be wrong with an eye's melanocytes. Heterochromia can also be the result of an individual's receiving different eye color genes. This can happen if two fertilized eggs become fused in utero.
Christopher Walken is one of a number of famous people who have heterochromia; one of his eyes is blue, the other is hazel.