Ever see one of those plastic cards with an image that changes when you tilt the card? That, my friend, was an example of lenticular printing.
How it works
A lenticular printed card has two components - the source images, and a ridged plastic covering which is actually made of many long, very thin (approx 0.3mm) lenses called lenticules. The source images are split into strips and arranged such that each lenticule covers several strips, one strip from each of the various images.
A cross section would look like this:
/\/\/\/\/\
OXOXOXOXOX
O = First source image
X = Second source image
/\ = Lenticule ridge
Thus, depending on the angle that the card is viewed at, one or other image is visible. This example shows only two images but more can be used. However, the more images there are, the more they tend to blur into each other. A usual amount is somewhere between three and twelve.
Lenticular printing can be used to create two different effects - depth or motion.
Depth
If the lenticules run vertically on the image, a primitive 3D effect can be created, by using source images that are pictures of the same object from different angles. Each eye sees the card at a slightly different angle and thus the lenticular printing effect can send the appropriately different source picture to the eye.
Compared to a hologram, a lenticular image is less impressively three dimensional, and presents a blurrier image. On the other hand, it can be in full colour, whereas holograms are usually monochromatic, and it can be seen in almost any lighting conditions, whereas holograms need to be precisely lit.
Motion
If the desired effect is to create the illusion of motion when the card is tilted, it is better to have the lenticules arranged horizontally. Otherwise the same effect which is useful for 3D will damage the movement effect as each eye sees a different frame of the animation.
Uses
Lenticular printing is used almost exclusively as an attention-grabbing gimmick. The eye is drawn to motion, or to mysteriously three-dimensional objects on flat cards, so it's very effective. As a result you tend to see lenticular printing used in advertising, or even directly on products, particularly those aimed at children such as breakfast cereals or comics. It can be used for decorative purposes too, and advanced techniques even allow for lenticular printing onto fabric such as T-shirts.
I'd like to thank amnesiac for goading me into writing this by insulting me repeatedly in the chatterbox.
Sources:
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How Stuff Works - http://entertainment.howstuffworks.com/question607.htm
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World Holographics - http://www.world3d.com/faqs.html