How does the Nintendo 3DS's 3D screen work?

The Nintendo 3DS produces the illusion of 3D using autostereoscopy. You can imagine the screen as showing two images at once, and having another screen (the parallax barrier) over it to only allow each eye to see one screen. Basically, the screen works by forcing each eye into seeing a different image. The screen has two images; each image is a different perspective of the same image, as if you were actually looking at a real object in real life. In real life, your eyes both see a slightly different perspective of the same object(s), and that provides the 3D effect, as abjects closer to you will have a bigger difference in the perspective. The same goes with the 3DS: it forces each eye into seeing a different perspective. and as a result, your eyes are tricked into seeing objects on the screen just as you see 3D objects in real life. It's all about making your left eye see the left side of the object, and your right eye seeing the right. That's what creates the illusion of depth.

If that's too confusing: it's magic. It's a magic screen.