a real world point of view
A grip is a member of the production staff tasked with ensuring the proper movement of the cameras during principal photography. He or she may have to lay dolly track, physically move or shake the camera, organise the use of cranes and perform any number of additional tasks so the camera operator can perform safely and accurately.
Though the position was never formally credited during the 1963 version of the show, grips would certainly have been needed to push the Television Centre's massive video cameras around. The leader of the grip team, known as the key grip has been credited in every live-action adventure since the 1996 telemovie, although in the BBC Wales version the key grip has been credited as a "grip". (Due to the differences between the North American and British film industries, however, the grip staff on the movie likely had to provide some of the electrical rigging work which is exclusively the province of the gaffer in British productions.)
Perhaps because of this slight difference in terminology, only the TV movie and Torchwood: Miracle Day have specifically credited a "key grip", making Dave Gordon the lone person to receive that credit in the history of Doctor Who. Only Miracle Day's Isaac Chee has received the credit in the 21st century DWU family of shows. It can be safely assumed that the BBC Wales on-screen credit of "grip" refers to the head of the grip department. The key grip reports directly to the director of photography and is roughly equal in production hierarchy to the gaffer. He or she generally has a best boy grip, who serves as the day-to-day administrator of the department, and will have an especially close working relationship with the gaffer's assistant, the best boy electric. However, the best boy grip has never been credited on screen in any Doctor Who production. The simplified on-screen credit of "best boy", a regular feature of the BBC Wales credit roll, refers exclusively to the best boy electric.
The work of grips hasn't often been highlighted by Doctor Who Confidential or Torchwood Declassified. However, grips can be seen working in the Confidential which accompanied School Reunion. There, viewers witness the grips laying dolly track for the pivotal poolside confrontation between the Tenth Doctor and Finch. Their work was also featured in the Confidential that accompanied The End of Time, Part Two, where director Euros Lyn describes how he achieved the "shaking" effect of Gallifrey descending upon the Earth.