Horizontal lens orientation is used when 3D is not required. Because humans eyes are stationed horizontally along the face each eye will have the same viewing angle of a horizontal lens. This means that both eyes see a single image, negating the brains natural tendency to perceive depth. Instead with each eye viewing the same image a user must move vertically (or rotate the piece vertically) to see change their angle of viewing through the lens and thus change the image that is visible. By quickly shifting through multiple viewing angles, and resultant images, a user can replicate a motion picture and achieve an animated art sequence.
Depending on the lens quality the animation can be anywhere from 2 to 40+ frames. A two frame animation is referred to as a “flip”. This is typically used in marketing gimics to show one image and then another. Other techniques include “morphs” which can be from as little as 3 images, with the start and end image being the same as were used in the flip, but intermediary images are some blurred or smeared combination of the two. The intermediary frames then work to simulate a morph effect. The same basic principle is used to create “zoom”, “spin”, and “fade” features.
Lensys, a lenticular company, has some great graphics showing the animation options available as does another site Big3d.com.
More on vertically oriented lenticular.