Red Eye

This effect is common when using a point-and-shoot camera with flash in low light. It's caused by the flash illuminating the blood vessels in the back of the eye, and is more common in small cameras because the flash is closer to the lens. It happens more in low light because the pupil of the eye is larger.

Cameras that have red eye reduction technology typically fire a few pre-flashes that cause the pupil to contract so that it's smaller when the photo is taken.