These have been around for a long time, and only people that are awesome have the ability to see the 3D images in the Magic Eye pictures.
You're supposed to cross your eyes or "look past the picture" to see the 3D image; it's difficult to learn, but once you do it becomes rather easy to see them, and you can focus on the image to literally make it crystal clear. You also will wonder how the hell it's done.
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Train your eyes by crossing them or "looking through" the image so the two small red squares merge to the middle, creating a third square, then look at the image itself. Even when you're able to see the 3D image it'll probably be a little blurry until you get used to it.
This one is an image of Saturn:
And I don't know what the hell this is supposed to be. Balloons I guess.
Got it? Good. Now try it without the training wheels.