Red-eye is actually light reflected back from your subject's eyes. The bright light of your camera's flash passes through the pupil of each eye, illuminating the blood-red retinal tissue at the back of the eye. This illuminated tissue , in turn , is reflected back into the camera lens. Red-eye problems worsen when you shoot pictures in a dim room, because your subject's pupils are dilated wider, allowing even more light from the flash to illuminate the retina .
If it's too late to avoid red-eye to begin with (by using an external flash, for example), and people's eyes are already glowing demonically, there's always iPhoto's Red-Eye tool. It lets you alleviate red-eye problems by digitally removing the offending red pixels. Here's how: