Tarragon is an herb. Some people call it âmugwort.â Be careful not to confuse tarragon with mugwort (Artemisia vulgaris). The parts of the tarragon plant that grow above the ground are used to make medicine. Tarragon is used to treat digestion problems, poor appetite, water retention, and toothache; to start menstruation; and to promote sleep. In foods and beverages, tarragon is used as a culinary herb.