Wiktionary
n. A system that allows a video version of a take to be viewed immediately after it is filmed.
Wikipedia
Video assist is a system used in filmmaking which allows filmmakers to view a video version of a take immediately after it is filmed.
Originally a small device, called the video tap, was installed inside a movie camera that allows (with the addition of a monitor) the director to see approximately the same view as the camera operator, and thus ensure that the film is being shot and framed as desired. This is done by using a small charge-coupled device (CCD) (similar to ones in consumer camcorders) inside the viewfinder. On modern film cameras, the assist is fed off a beam splitter, which splits the beam between the optical viewfinder and the video tap. The light enters through the lens, and hits the rotating mirror shutter, which bounces the light to the horizontal ground glass. The beam splitter is directly over the ground glass and turns the light again 90 degrees, and projects it onto the chip of the video assist camera—through its own lens system. The chip, together with its electronics, lens system and mounting hardware is the video tap, and was commonly called video assist until the video assist industry grew large.