Originally used mostly in novelty items and commonly called "flicker pictures" or "wiggle pictures" lenticular printing is a technology in which lenticular lenses (a technology that is also used for 3D displays) are used to produce printed images with an illusion of depth, or the ability to change or move as the image is viewed from different angles. (source: wikipedia)
The image below is a quickly animated gif that I created from a recent listing appearing on ebay for a 1950's child's novelty ring.
A quick google search for lenticular imagery (or the wikipedia link above) will direct you to tons of interesting new and vintage uses of this technique. Here is one link to a gallery of vintage imagery on pinterest: https://www.pinterest.com/ohbyjingo/action-vintage-lenticular-pictures/