A deleted scene refers to footage that has been removed, censored, replaced, or simply left out from the final version of a film or television show. (It is occasionally referred to as a "cut scene", however the different usage of this phrase in reference to video games makes this term uncommon in this context.) A related term is "extended scene", which refers to the longer version of a scene which was shortened for the final version of the film. Often extended scenes will be included in collections of deleted scenes, or also referred to as deleted scenes themselves, as is the case with for instance, Harry Potter and the Chamber of Secrets and Serenity.
Scenes are removed, replaced, or shortened in films for a variety of reasons, including:
The studio or network that is providing funding/support for, owns the rights to, or plans to air or distribute the film(s) (usually the prior two) may be uncomfortable with a certain scene, and ask that it be altered or else removed or replaced entirely.
This kind of situation is most common in the production of television series, since networks and channels often have to be mindful of how the viewers, critics, and/or censors will react to programming, and may fear losing ratings, incurring fines, or having trouble finding advertisers.
Concerns about running time can also be cause for removal or shortening of scenes.
In feature films, sometimes scenes are cut to keep the length of the film's theatrical cut shorter. This has apparently happened with most of the Harry Potter feature films, including an arguably important transitional/plot-related scene in the second film (involving Harry's overhearing of the conversation in the shop in Knockturn Alley), which was not in the theatrical cut but was released on the 2-disc DVD along with several other deleted scenes.
In the movie Terminator 2: Judgment Day, the scene showing John Connor reprogramming the Terminator was shortened by deleting dialogue which made other scenes necessary, and these scenes were left out of the theatrical release version (but restored on the special edition VHS). Also, a scene where the T-1000 kills the family dog was deleted. In interviews, both Schwarzenegger and Cameron stress this was done to shorten the film (the theatrical version still ran 2 and 1/2 hours, even without these scenes), but these scenes were not restored for the DVD set released in 2003.