It relies on the phenomenon known as persistence of vision. Once the eye sends an image to the brain, we maintain that image for some time before it's supplanted by the next image. So, if you see a series of still images quickly enough, and there's a small amount of difference between each image, we perceive that as a single moving image.
A zoetrope is also simple and simple to make. It's just some kind of drum with an open top (an empty ice cream container works well and it's fun to empty) and a series of images drawn on the inner surface, alternating with slits to view the animation. It works best if there's a drawing directly across from a slit.
Another approach is to put the drawings beneath the slits. That way you have more slits and more drawings, but it forces you to view the animation at an angle and is more suited for a larger zoetrope.
The most difficult part of making a zoetrope is creating the paper strip animation, so we've done that for you as a downloadable Adobe Acrobat PDF. You can enlarge the drawing on your printer for a larger zoetrope.
Of course, you can just ignore our simple zoetrope for something more sophisticated, so we encourage you to experiment. Probably the best zoetrope you can make is that ice cream container with the slits and drawings resting on an old record player turntable.
There are several websites with information about zoetropes and other early animation devices, including:
Make Your Own Zoetrope (Digital Studio)
Build Your Own Zoetrope (Freeweb)
and a kit you can buy:
Random Motion (animation by Ruth Hayes)