To be able to see these images, your eyes have to pretend they're looking far away but focus on a closer object. If you are looking at the image normally, your eyes are focused and converge at the distance the image is from you. To see the autostereogram's 3D image, your eyes are focued at the correct distance, but are converged at a different distance (infinity), making the image hit your eyes at the "wrong" angle. Each eye is looking at a different part of the picture, which is why the edges never look right. Your brain sticks everything together, thinking that you're seeing a 3D image but in reality you're just looking at it all wrong.
In a simple "wallpaper" type of autostereogram, they take a repeating pattern or two to trick your brain into making you perceive them as being on a different plane than the background.
The tiger is repeated every 120 pixels, the shark every 130 pixels, and the person riding the tiger every 140 pixels. So, when your eyes go all crazy, the tiger seems closest, the shark is farther away, then the person riding the tiger is on the background plane.
Then if you mess with size and spacing and such, you can do all sorts of crazy things. For example here is a bunch of tigers at different depths. This image shows you how the spacing of the pattern affects the depth you perceive.
So of course no one wants to sit down and make these, so they made a computer program that builds these images for you. This program takes a grayscale image of the image you will see in 3D and a random dot pattern, then figures out how to adjust each reiteration of the pattern to make you see the 3D image.
And of course, someone figured out how to go too far with this.
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