Pupil size/Flash. The "red eye" is caused by light from the camera flash reflecting off of the retina in the back of the eye through the pupil. This will only occur if the subject has large/dilated pupils and the flash is used. Most of the time if you are using the flash, you are in a dark environment so the pupils will be larger than average.
Pupil size. Red eye is the actual color of the back of the eye. It appears black because the light behind your head is blocked by your head and no light escapes the eye you are looking at. In a flash photo, the light source is almost in line with the lense and so red eye can occur. It is more likely if the pupil is larger and in kids because they like to look at lights. Adults look away if possible.