An herb, Artemisia vulgaris, named after Artemis, goddess of the hunt and the moon and patron to women, or perhaps after Artemisia, botanist and queen. That's the Latin name. Its English name may derive from the fact that it used to be used, as hops is today, as a bittering agent for beer, or perhaps from the old English word from mucgwyrt (mucg, insect; wyrt or wort, plant), as smudges of mugwort can be burned as an insect repellant.
Mugwort grows freely throughout Europe and Asia; it's a perennial that can grow up to 3 feet (1 m) in height. It has dark green leaves on top with a silvery underside, and small green flowers which appear early in the fall. It propogates itself with abundant seeds or rhizomes and will take over an abandoned area with ease and speed.
Mugwort leaves and rhizomes have long been used for medicinal and other purposes. Romans apparently placed it in their sandals to protect their feet, and according to legend John the Baptist wore a girdle of mugwort when he lived in the wilderness (which must have looked rather silly); thus it's sometimes also known as St. John's herb. Mugwort was one of the nine healing herbs of the Anglo-Saxons; they used it to treat ringworm, threadworm, and insect bites; to speed delivery of the placenta or as an abortifacent; and to treat infections, including fungal ones. It is bitter and pungent and will repel moths and cockroaches. In spite of (or perhaps because of - tastes vary across culture and history) its bitterness, it was added in Europe to foods like dumplings, sausage, duck and eel, apparently because it counteracts the effects of fatty food. Mugwort apparently aids in lucid dreaming, and mugwort pillows were common during the Renaissance period in Europe.
In China, mugwort has been used in a dried compacted form known as moxa for a few thousand years, even longer than acupuncture. Moxa is generally a rolled cylinder of the shape and size of a cigar; you can also obtain smokeless moxa, which contains compacted mugwort and looks kind of like huge sticks of incense. In this form it's often used for direct moxibustion: the moxa is placed directly on the skin and burned, causing blistering and burns, after which scabs will form. The idea is that pain is caused by blocked qi and blood; the heat of the moxa stimulates the flow, thus relieving the pain. In the west, where we're a bit squeamish about this kind of painful intervention, it's more common to use indirect moxibustion: the moxa is separated from the skin by some kind of medium, such as a glass dish, garlic, ginger, or air. In the case of air, the burning moxa is held close to the body, causing the skin to redden and the flesh to feel hot. Moxa can be used for any stiff or achy joints, and to relieve arthritis pain. Burning moxa on salt in the navel is apparently an instant cure for diarrhea, and I'd think a quick recipe for a burnt belly button.