Lovage is a plant. The root and underground stem (rhizome) are used to make medicine.
Some people take lovage by mouth as "irrigation therapy" for pain and swelling (inflammation) of the lower urinary tract, for preventing of kidney stones, and to increase the flow of urine during urinary tract infections. But there is no good scientific research to support the use of lovage for these or other conditions.
In foods and beverages, lovage is used for flavoring.
In manufacturing, lovage is used as a fragrance in soaps and cosmetics.