If you abuse someone, it means you are hurting that person, mentally, emotionally, or physically. If someone else is harming you, you are yourself suffering from abuse.
The word abuse is made up of two parts — "use," which means to employ, and ab-, a Latin prefix meaning "away" — and as a whole comes from the Latin abūsus, meaning "misuse," or "use wrongly." It began as a verb and became a noun in the mid-15th century. Abuse also refers to anything that is employed improperly or to excess, such as the abuse of alcohol or drugs.