Officer Big Mac was created to personify McDonald's Big Mac. The character was depicted as a police officer with a Big Mac for a head, making the sandwich itself the defining visual clue.
Officer Big Mac belonged to the wider McDonaldland cast, where food-based characters helped make specific menu items memorable. His police-officer role also provided a contrast with the Hamburglar, whose stories often involved trying to get hamburgers.
The character is easily confused with Mayor McCheese because both had cheeseburger-like heads and appeared in the same advertising universe. Their roles were different: Mayor McCheese represented a civic leader, while Officer Big Mac represented the Big Mac and served as a law-enforcement-themed character.