The span of distance along the shot axis in which objects will be in focus. Determined by focal length and iris aperture.note
Skillful management of this property is a requirement for Rack Focus.
A shallow Depth of Field might be used for scenes set in restaurants and other public settings to keep the background blurry, and thus de-emphasize it for intimacy's sake (or to blur out people in the background that might oppose to having their picture taken, especially common on shows like Law and Order which frequently film in crowded areas full of non-acting people.)
2001: A Space Odyssey, Star Wars, and the '80s version of Battlestar Galactica were innovative in that the models of the spaceships looked like large ships that were far away. Among other things, small lens apertures to lengthen the Depth of Field strengthened the illusion.
Long depth of field is sometimes faked by Forced Perspective — having an object in the foreground be an oversized prop. An example would be the One Ring lying in the snow in Fellowship. The prop ring for that shot was the size of a plate.
Modern video games attempt to emulate the depth of field effect of a real camera via a number of post-production effects, some of which are quite adept while others decidedly less so. More traditional forms of art can play about with it using Graphical Perspective.