There are masses of photographs on the internet of cats that have been taken with flash on the camera.
When the flash is on the camera the light from the flash reflects off objects at an angle which results in the reflected light returning close to or at the position on the camera lens.
If you are photographing a cat this way you often get a picture of a cat with laser eyes and a funny cheeseburger caption. You get "red eye" when the same thing happens to a person.
Why are cat's eye reflections brighter? This phenomenon has been known for decades hence the term "cats eyes" when referring to the center lines on roads (there are much fewer than years ago).
The reason is bound up with the cat's ability to see better in the dark than humans. Behind the retina of the cat's eyes is a reflective material which is designed to boost the image received by the eye. In modern parlance it is an image intensifier.
Human eyes reflect red (the color of blood, which feeds the retina). For the cat it is a bright light from this reflective material.
When it is completely dark, however, cats can't see in the conventional sense. They fall back on their other outstanding senses namely smell, sound and her sensitive whiskers that detect air currents.
Photographs reproduced under creative commons. Copyright (top) Maggie Osterberg (bottom) r11132a (Flickr)