It requires a motion picture camera that can expose single framess. It works by shooting a single frame, stopping camera to move the object a little bit, and then taking another photograph. When the film runs continuously, it appears that the objects move by themselves.
This is similar to the animation of cartoons. The great American pioneer of this technique was Willis O'Brien, who animated King Kong. His student Ray Harryhausen made a number of movies with the same technique. More recently, stop motion has been used in the works of Aardman Animation, including the Wallace and Gromit films as well as their film Chicken Run. Aardman also produced commercials and music videos, notably the video for Peter Gabriel's "Sledgehammer", which uses a variant of stop motion called pixilation; this involved Gabriel holding a pose while each frame was shot and moving between exposures, effectively becoming a human puppet. More recently Aardman used this technique on a series of short films for BBC THREE entitled Angry Kid, which starred a live actor wearing a mask. The actor's pose and the mask's expression had to be altered slightly for each exposure.
Another variation on stop motion is "go motion", used on the film Dragonslayer, which involves moving the model slightly during each exposure to produce a more realistic motion blurring effect.
Nowadays the almost universal use of computer generated imagery has effectively rendered stop motion obsolete as a serious special effects tool, although it is still widely used on children's programming, commercials, and the occasional comic film.
You can try stop motion on your own with most ordinary video cameras. Use a tripod, a chair or something else to secure the camera, toggle recording modes until you find the appropriate mode, and start shooting clay models, action figures, or whatever you wish.