Three little kittens

Why do their eyes glow when their photo is taken with a flash?  Couldn't find an answer specific to cats, but here's the fascinating explanation for dogs (and for red eyes in photos of humans):

In dogs (and many other animals, but not people), the retina has a reflective layer behind it called the tapetum lucidum, which acts like a mirror, reflecting light at the back of the eyes. The reflective layer is what helps dogs see better at night. Light is reflected outward, giving the dog's retina a second chance to absorb the rays.

This is what takes place when you snap a flash picture of your pet, and it’s why your dog’s eyes may take on a creepy glow. Individual dogs have different colored tapetum, which is why some dogs’ eyes take on a green glow, others a yellow glow, and so on.

If your dog consistently has red-eye in photos, he might not have pigment in the tapetum. This means the red is coming from blood vessels at the back of the eyeball, which is also the cause of human red-eye.