A bodyguard was a person, or sometimes a group of people, employed to protect someone.
In the alternate timeline where Biff Tannen had used a sports almanac he received from his older 2015 self to successfully bet on sporting events and amass a fortune, his gang from 1955 — Skinhead, Match and 3-D — were working for him as bodyguards at Biff Tannen's Pleasure Paradise Casino & Hotel.
After finding Marty McFly in the Biff Tannen Museum, the gang knocked him out and took him upstairs to the twenty-seventh floor where Biff had his penthouse. After Marty confronted Biff about the almanac and escaped, Biff went to the telephone and ordered his bodyguards to take care of Marty permanently.
Marty managed to give the gang the slip in the hotel stairwell by hopping the railing to get to another staircase leading to the roof, while the three men continued to run down the stairs.