Re how they work – you’ve got two eyes, right. They can be focused on something either close or far away – focus on somethign close then the far away stuff looks fuzzy, and vice versa.
Each eye sees a separate image, you see two at a time and your brain merges them. However, when looking at something both eyes have to point at the object so that the two images overlap and your brain can merge the two images to get a 3d picture.
If your eyes are pointing at something further away and something closer is in your field of view you’ll see two of that thing, but blurry – look at your computer screen and put your finger 8″ from your face – two fingers.
Magic Eye requires you to learn the trick of focusing your eyes on the page but having the lines of sight from each eye converge at a different point, behind the image. This results in two overlapping images like your finger, but they’ve carefully made the pattern of dots so that when you overlap them they make another picture. But because each eye is seeing something slightly different your brain merges them and constructs a 3d image – because each different image is carefully calculated.
Got that? Good.