A heavy medieval war club with a spiked or flanged metal head, used to crush armor. Note that real maces are illegal in NSW. The point of it was to emulate a club, but with more weight and, optionally, the sharp edges of the spikes or flanges for concentrating force. Both infantry and cavalry used them -- the horseman's mace tended to be shorter in the shaft, for easier wielding; the footman's longer for added power (albeit at the expense of speed).
Mace is an aromatic spice that originally came from East Indonesia. Dried and leathery, mace has a very similar flavour to nutmeg, which isn't surprising. They're both sourced from from the same plant - nutmeg is the kernel of the fruit, mace is the lining that separates the kernel from the pulp.