This is known as lenticular printing.

From Wikipedia: How It Works

Each image is arranged (slicing) into strips, which are then interlaced with one or more similarly arranged images (splicing). These are printed on the back of a piece of plastic, with a series of thin lenses molded into the opposite side. Alternatively, the images can be printed on paper, which is then bonded to the plastic. With the new technology, lenses are printed in the same printing operation as the interlaced image, either on both sides of a flat sheet of transparent material, or on the same side of a sheet of paper, the image being covered with a transparent sheet of plastic or with a layer of transparent, which in turn is printed with several layers of varnish to create the lenses.

A close up of the surface of a lenticular printed 3D image.

To see how movement changes the image you see, this diagram shows it pretty effectively.