What is a picture within a picture called?

A picture with a smaller version of the same picture within it is known as the Droste effect. The word comes from the Dutch.

The Droste effect is recursive and will give the illusion that the image inside the image goes on to infinity. In reality, the succession of images can only go on as long as the overall picture's resolution allows.

A stereogram is another type of image inside another image. In a stereogram, a three-dimensional image is hidden inside a larger picture. The three-dimensional image can be seen by staring at the picture. Slowly the eye will begin to see the hidden image.