The thaumatrope (from the Greek "thauma" meaning "wonder" or "marvel" and "tropos" meaning "to turn") was a 19th century children's toy that actually began as a scientific experiment by physician John Ayrton Paris in 1825 (the invention of the thaumatrope is sometimes credited to others, but it is generally agreed that Paris was the first to make it popular).
Paris was exploring a concept called "persistence of vision," first identified by Peter Roget in 1824. The human eye collects light, which causes a reaction in the light-sensitive receptors in the retina. This process happens almost instantaneously. However, according to the theory behind persistencen of vision, this chemical reaction cannot be halted as quickly as it was initiated, causing perceived overlap in a succession of static images.
In an attempt to prove the existence of persistence of vision, Paris took a small piece of stiff paper, drawing a canary on one side, and an empty birdcage on the other. He attached lengths of string to opposite sides of the paper, and repeatedly twisted the string until it was taut. Having set up the experiment, the two lengths of string were pulled in opposite directions, causing the piece of paper in the middle to rapidly spin. Because of persistence of vision (or so Paris thought*), test subjects saw a single image of a canary in a cage, instead of correctly distinguishing the existence of two separate images. When Paris began marketing the thaumatrope commercially as a children's toy, many variations on the original choice of images appeared. Some of the most popular choices included a horse and its rider, or a bare tree and its leaves.
The thaumatrope passed from the world of science into the world of toys with ease - a fact that caused some controversy within academic circles. Charles Babbage, in particular, criticized Paris for popularizing the device as a toy for reasons of personal profit. Babbage credited friend and colleague John Herschel as the originator of the concept of a thaumatrope, but implied that the learned man was far too occupied with more important matters to busy himself with actually building (let alone selling) such a trifle. In his contentious work Reflections on the Decline of Science in England, Babbage seizes upon Paris and his toy as an embodiment of the shoddy treatment of those who pursue abstract science, stating that, "the contriver of a thaumatrope may derive profit from his ingenuity, whilst he who unravels the laws of light and vision, on which multitudes of phenomena depend, shall descend unrewarded to the tomb."
While the thaumatrope may have held limited value for the realm of abstract science, it was not quite as useless as Babbage believed. By proving the existence of persistence of vision (or at least something very much like it), the thaumatrope provided a practical basis for continued research into the phenomenon, leading to the invention of devices that could produce the illusion of motion. The principles learned from these endeavors, when coupled with advances in photography, eventually evolved into modern motion picture technology.
* For nearly 150 years, persistence of vision was held responsible for optical illusions as simple as the one produced by the thaumatrope, and later, as complex as motion pictures. This influential theory was proven false in the 1970s; the thaumatrope actually relies on the brain's inability to correctly process the images, rather than the eye's inability to correctly perceive the images as distinct. However, the inventor of the thaumatrope certainly believed that his device exploited persistence of vision, and so this information is included as a matter of historical context.
Sources:
http://courses.ncssm.edu/gallery/collections/toys/html/exhibit06.htm
http://www.anotherscene.com/cinema/pov/thauma.html
http://easyweb.easynet.co.uk/~s-herbert/dr_paris_thaumatrope.htm
http://encyclopediaoftheself.com/classic_books_online/dosie10.htm
http://www.acmi.net.au/AIC/MAGIC_MACHINES_2.html