Plasticine itself was invented in 1897, and makes Claymation possible. Though it can be manipulated like clay, it doesn't lose its plasticity or harden over time. This makes it ideal for animation because the animator can use it over and over again, instead of having to start again from scratch whenever the clay dries out.
The medium itself can be combined with the technique of stop motion to create animation on film. The plasticine (or multiple pieces of plasticine) are formed into the shape of a figure, which is then photographed. The figure is then moved ever so slightly and photographed again, then moved a little more and photographed again. When strung together, the model appears to move. Note that stop-motion can include figures not necessarily made of plasticine: jointed dolls, for example, which were used in movies such as "King Kong" in 1933 and "The Nightmare Before Christmas" in 1993.
Claymation isn't necessarily expensive, but it is incredibly time-consuming. The stop motion process entails 24 separate movements for each second of completed film--and if the animator makes a mistake, the resulting animation will appear clunky or disjointed. Claymation animators and similar stop-motion artists thus tend to be extremely patient and devoted to their work.
Will Vinton and the animators in his studio are among the most noted practitioners of Claymation. Their most famous creations are the California Raisins ads of the 1980s, which turned into a phenomenon and helped elevate the medium in the public eye. Vinton himself has trademarked the term "Claymation," and while numerous other animators practice similar techniques using plasticine, technically only animation produced by Vinton studios is "Claymation."
Vinton is hardly the only artist to excel at the format, however. The first true pioneer was artist Art Clokey, who used Claymation to produced Gumby and Pokey in the late 1950s. And though Vinton studios continues to produce top-quality work, it has since been eclipsed in the public eye by Aardman Studios in Great Britain--whose films (many of which feature their beloved creations Wallace and Gromit) have generated multiple Academy Awards.