So back about 300 or so years ago the European convention of indicating their position or importance in society by wearing wigs was widely accepted. The bigger the wig - the more important you were. A captain at sea would wear a larger wig than his officers. So he was the Bigwig on board.
Mike is nearly bald, so Brenda must be the Bigwig aboard Wrinkles. I guess that is why we refer to her as the Admiral.