A lenticular is a combination of a special lens and an arrayed image that simulates animation or depth. Autostereoscopic images refer to pictures that take advantage of how our eyes and visual cornea process the two images that the left and right eyes receive. They interpret them as depth and 3-dimensionality. A lenticular uses the movement of our bodies in relation to produce a pseudo-hologram that might look like a person running, an apple popping out of a flat poster, or a distant car approaching.
There are two parts to a lenticular. The lenticules, or the series of elongated plastic lenses, focus, magnify, and direct the right parts of the picture to your eyes. The interlaced background image (apart from an overlaid lenticule) looks like a jumble of several pictures. Actually, the assembly is made of stripes of a number of images divided vertically or horizontally that are interlaced such that only one slice of each image lies behind each lenticule.
The various images are revealed in sequence to the viewer as you look at the picture from different angles, such as walking by a poster or tilting a hand-held card. The lenticular controls which slices you see at which angle, such that together you are only seeing one reassembled, whole image at each point in time. Through rapid movement, or with smaller lenticules, the images blur together into depth or motion.
A lenticular image is capable of simulating many different kinds of movement, depending on how many pictures are interlaced and how the pictures relate to each other. In zooming, the pictures will be of the same object taken from different distances. With motion, the pictures will differ by time, such that a ball goes from the ground to a foot off the ground to eye level, similar to cell animation, to make it bounce. A morph is a variation of motion, where one object gradually turns into another one, such as purse that becomes a shoe.
A "flip" only uses two images that are thematically related, such as a bag of popcorn and a movie ticket, to associate them in your mind. Depth and 3-D are related. The constituent images are of the same object taken at different angles, but at the same time point. This means one eye will see one perspective, the other eye a slightly angled perspective, and together they will create depth.