They are assistants to their department heads, the gaffer (in charge of electricals) and the key grip (lighting and rigging), respectively.
Their many responsibilities include the hiring, scheduling, and management of crew; the renting, ordering, inventory, and returning of equipment; workplace safety and maintaining discipline within their department; completing timecards and other paperwork; stocking of expendables; loading and unloading production trucks; planning and implementing the lighting or rigging of locations and/or sound stages; coordinating with rigging crews and additional photography units (if applicable); handling relations with the other production departments; overseeing the application of union rules (where relevant); and serving as the day-to-day representative of the department with the unit production manager and coordinator of their department.
Large-scale productions such as major films commonly include full-time rigging and second unit crews, and in total may hire many dozens of grips or electricians at one time.
According to the OED, "It has been suggested that it originated as a term for a master's most able apprentice, or alternatively that it was transferred from earlier use for a member of a ship's crew, but confirmatory evidence for either of these theories appears to be lacking.
"[citation needed] The earliest known appearance of the phrase in print is 1931 from the Albuquerque Journal: "Among the electricians ... the department head is the gaffer, his first assistant is the best boy.