The mace consisted of a flanged head on the end of a long handle. The more intricate the design, the more prestigious the man wielding it would have been.
A mace can refer to any solid club; however it normally refers to those with metallic heads from the Medeival era. A flail is not a mace: as flails use chains or rope to make the head of the weapon spin and thus impact with greater force. A Morningstar can be either a mace or a flail.
As muskets rose during the renaissance, armor began losing its relevance on the battlefield, and thus; the mace was no longer used by the common soldier. Muskets themselves could be used as clubs. However the mace returned to the battlefield with the beginning of trench warfare; as soldiers were forced to engage in close combat within the trenches. Most of these clubs were improvised; chairlegs, wooden planks, scrap-metal, Baseball Bats, ect... Some gurellia fighters, criminals and terrorists use clubs as well; though this is rare.
The flanges concentrated the force of the blow on a smaller area, giving it more power. It would have been used from horseback or on foot, with the former having a longer handle. The bludgeoning force of the weapon was strong enough to kill a helmeted opponent due to a broken neck when it struck the helmet. In the show the Iron-Flanged Mace shattered one ballistics gel skull and two synthetic bone skulls in 16 seconds, with a force of over 300 psi.
Maces were designed to fight against plate or heavy armor; which had few gaps and could withstand the blows of lighter weapons. Knights commonly used maces for this purpose; but blunt weapons were also popular as many Christians were disgusted by the spilling of blood. Bishops and clergy willing to defend themselves from enemy invasions went to war wielding maces and flails.