Pushing film is a term for rating the ISO film speed higher (faster) than the film is designed for. Many films may include an exposure index (EI) rating in addition to the ISO film speed. For instance, an ISO 100 film can be rated 200 or 400 depending on the film brand. Pushing film is simple. If a photographer is using 100 ISO film, they can set the film speed of the camera to something higher, like 200 or 400. By pushing film to a faster speed, you will gain faster exposures. This is helpful in situations where you only have a certain film speed but need to shoot fast moving subjects, like wildlife photography or motion photography, or find yourself in low-light situations. It is extremely important to note, however, that you cannot change the ISO in the middle of a roll. When you push film, you are basically underexposing the film by a stop or two, so when processing the film in the darkroom setting you must add additional time in the development process to ensure your film is developed properly. If you change the ISO film speed in the middle of a roll, half the roll will remain underexposed while the second half is properly exposed. Read more about push processing in the film processing section of this site.
Some films, including ISO 3200, are actually push films. The true ISO of these films is somewhere around 800 to 1000, but are designed to be pushed up to 3200 for low light conditions or fast motion photographs. Note that pushing film beyond the ISO speed, particularly with high speed films, will increase grain in the film and the subsequent prints.
Pulling film is just the opposite of pushing and is much less commonly used. Pulling film is essentially rating film lower (slower) than its intended ISO speed, for instance pulling a 400 ISO film to 200 to slow exposure by one stop and overexposing the film. Pulling film is mostly done to reduce contrast in high contrast environments. It should also be noted that pulling 3200 speed film does not actually pull the film. Because 3200 film is a push film, pulling the film back to 800 or 1000 ISO is actually exposing the film at the ideally rated ISO speed. For more information about processing film that has been pulled, see pull processing.