A hidden 3D image is what you can find in a stereogram if you know the proper way to look at it. When we look at something our eyes look at the same spot on a surface of an object. Our brain then calculates the distance to the object based on the positions our eyes have taken. But when we look at a stereogram (the proper way) our eyes look at two different spots on the surface but the pattern on these two spots are the same, so our brain think that it is the same spot. Consequently our brain calculates a wrong distance and it seems to us that we are not looking AT the stereogram but instead that we are looking at something BEHIND the stereogram. That is how stereograms works.

I've made a few stereograms which you can see in the stereogram gallery. If you want to make your own stereograms, read the tutorials and get a stereogram generator. I suggest SISGen 1.58. It's not fantastic, but it's the best I could find. See the links below.

SisGen 1.58 is a pretty old program, but it's the best stereogram generator I could find. You can download it from here and there are also some information resources.
Stereograms, stereogram generators, and more.