What causes red eye when you take a flash photograph?

There's lots and lots of blood at the back of the eye. When you take a photograph, the flash goes into the eye, illuminates the inside of the eyeball, illuminating that bright red, dark, rich red blood, and the light then comes back out of the eye towards the camera through the very big open pupil, and the camera picks it up, which is why your eyes look red.

If you have red eye reduction, what that does is to give a little pulse of light first which causes you to close your pupil, so the amount of light from the flash that can get in to the eye in the first place is reduced, and that cuts down the problem.