A wide-angle lens has a short focal length, which exaggerates the relative size of objects within field of view.
All other conditions being equal, wider lenses also affect both the angle of view and depth of field for a shot. That is, for a given camera position, a wider angle lens increases the angle of view available in a shot. And for a given aperture setting, wide-angle lenses tend to increase depth of field.
Taken together, to the extent that both the foreground and background appear to be in focus, these effects of a wide-angle lens tend to privilege staging within a shot, potentially leading to longer takes, allowing the viewer’s attention to wander over the image. Andre Bazin points to Citizen Kane, and in particular to Susan’s attempted suicide scene, where Greg Toland’s use of the wide-angle lens allows Welles to stage dramatic tension in three planes within one frame.
Because of how much visual information wide-angle lenses can capture, they are often used in establishing shots. In classical Hollywood film style, establishing shots are often the shots that open the scene: they show the entirety of the space where the scene is taking place, including geography and spatial relation between subjects. Wide shots can sometimes also give the audience a breather from the tension of a scene, whereas closer shots force the audience to focus on a particular subject.
The one feature of wide-angle lenses which does not depend on other conditions is that they exaggerate depth. A wide-angle lens will make subjects feel far apart from each other, giving a sense of a distorted or weirdly massive world; when used in a closeup, wide-angle lenses can distort the features of the subject. Sometimes this distortion is used for narrative purposes. Filmmakers notable for this technique include Wong Kar-wai (Fallen Angels), Darren Aronofsky (Requiem for a Dream), and Terry Gilliam (12 Monkeys). Recently, filmmakers such as Peter Jackson have used this property of wide angle lenses to stage characters of very different sizes within the same scene, using optical, not CGI effects (Lord of the Rings).
The technical definition of a wide-angle lens, in film cinematography, is that its focal length (measured in mm) is significantly less than the diagonal of that of the film frame in use.
Apparent wide-angle exaggeration is dependent on the format being shot on. In film, a wide angle lens will produce different effects with different frame formats (or film stock): Super 8 stock, 16mm stock, Super 35, 35mm, etc., will make lenses with different focal lengths count as wide. The frame formats describe the area of film stock exposed per single frame. Although a 24mm lens is wide (though not extremely so) in Super 35, it is actually a telephoto lens in Super 8. Similarly in digital cinematography, a lens is judged “wide angle” by relating focal length to receptor size.
Furthermore, the “wideness” of a lens is to some degree subjective. The 50mm lens is nominally the “normal” lens on a 35mm camera, the lens which renders perspective most similarly to the human eye. Robert Bresson was notable for his heavy preference for the 50mm lens. Some directors, however, feel that wider lenses (such as the 40mm or 35mm) actually recreate human perception more naturally. Gordon Willis, cinematographer of The Godfather and Manhattan, among other films, was heavily reliant on the 40mm lens.