In
cinematography, a shot from the
point of view of a character, ie. appearing to be through his or her (or its) eyes.
Because the camera is necessarily at or near eye level, and is often rolling or bobbing in a way to convey the subject's gait, this shot involves the viewer more than a static shot and can be used to create tension and anticipation as well as the obvious identification of the viewer with the character.
Stavr0 points out that such a shot might also include the subject's hands, shoes, tools or weapons.
First-person shooter games are all subjectively shot, which is part of why they're so
gripping.