Wiktionary
n. A member of a film crew responsible for maintaining the film's internal continuity and for marking the production unit's daily progress in shooting the film's screenplay.
Wikipedia
A script supervisor (also called continuity supervisor) is a member of a film crew and oversees the continuity of the motion picture including wardrobe, props, set dressing, hair, makeup and the actions of the actors during a scene. The notes recorded by the script supervisor during the shooting of a scene are used to help the editor cut the scene. They are also responsible to keep track of the film production unit's daily progress. The script supervisor credit typically appears in the closing credits of a motion picture and is listed on IMDB under Misc. crew, even though they have a crucial role in the shooting of a film.
In the most basic description, the script supervisor is the editor's and writer's representative on set, as well as being the right hand aide to the director and the director of photography. It is the script supervisor's job to make sure that at the end of the day the film can be cut together. In that sense, they back up every department, monitor the script during shooting and make sure that errors in continuity do not occur that would prevent the film from being able to be compiled smoothly in the editing room.
In pre-production, the script supervisor creates a number of reports based on the script, including a one-line continuity synopsis providing basic information on each scene such as the time of day, day in story order, and a one line synopsis of the scene. These reports are used by various departments in order to determine the most advantageous shot order and ensure that all departments, including production, wardrobe, set dressing, hair and makeup, are in sync in regards to the progression of time within the story.
Usage examples of "script supervisor".
The girl with the clipboard is Penny Fulweider, she couldn't quit working even if she wanted to--she's the script supervisor.