Something that's alcoholic contains alcohol. At a party, the host may offer a pitcher of alcoholic punch and another of non-alcoholic punch.
Use alcoholic to describe something that has alcohol in it, or otherwise has to do with alcohol. Alcoholic cider, for example, is fermented, and drinking too much can be intoxicating. The noun alcoholic means a person who's dependent on alcohol, whose drinking has become compulsive and unhealthy. This meaning developed in the late 1800s, from the earlier term alcoholist. The group Alcoholics Anonymous was founded in 1935 for alcoholics to help themselves and others quit drinking.