When the strings are twirled quickly between the fingers the two pictures appear to combine into a single image due to persistence of vision
Persistence of vision - the eye's ability to retain an image for roughly 1/20 of a second after the object is gone.
The eye continues to see the two images on either side of the thaumatrope shortly after each has disappeared. As the thaumatrope spins, the series of quick flashes is interpreted as one continuous image.
Stop-motion is a form of animation that relies on photographs of still objects to create movement. Objects are manipulated and photographed sequentially. When the photographs move together in a quick sequence (like in a film) it creates the illusion of movement. This is similar to the way a flip-book works.
Clay figures are often used in stop-motion for their ease of repositioning. Stop-motion animation using clay is called clay-mation.