Stereoscopic 3D has been around for a very long time. Many of us had toys that used the effect when we were kids in the form of a View-Master. The way the 3D works is that two nearly identical images are presented, one to each eye. Your brain combines the images into a single image, which creates depth in the single image. The reason the depth effect works is because each image is slightly different from a perspective standpoint, and when the image is fused in your brain, both perspectives are preserved, making the scene look alive.
Below I have a good example piece. To make it work you’ll have to cross your eyes until you see a 3rd image between the two. Focus on that 3rd (middle) image and it should come into focus. You may have to get closer to your monitor (10 to 12 inches) to make it work. If you do it correctly, the image should clarify and show depth to it. Try it now.
Now, the 3DS works in the same way, but the cool thing with Nintendo’s technology is that the LCD screen sends the images to your eyes without you having to do any headache-inducing eye crossing. The result is a constant and moving image that has a great sensation of depth. The slider for increasing or decreasing the 3D effect is simply affecting how much the two images vary from a viewpoint difference, making the fused image seem more or less pronounced in its depth.