Quick explanation:
When you watch a 3d movie, it switches very quickly between images for your left and right eyes. Think of those red and blue 3d glasses. The image for the right eye is bluer, (or red, whatever it is) so it gets blocked by the blue lens. That way, only the correct image gets to the right eye.

The 3DS works a bit like that, but it directs the image for the right eye ONLY toward the right eye. That's how it keeps the images seperate. I suppose that it could use the camera and face detection to do this more acurately.