A mace was a short, club-like weapon that inflicted heavy damage by sheer force, not cutting ability. The blunt hit of a mace could injure a warrior in chain mail, while a sword might not penetrate the same armor. Also, a well-placed mace blow could crush plate armor, while a sword blow would often deflect off of the smooth surface.
A flanged mace was a type of mace that had short projections from the head called flanges. These flanges could concentrate the force of the blow into a much smaller area, making it possible to break armor where a normal mace could not.