A digestif is an alcoholic drink served after a meal, traditionally believed to aid digestion - the name comes from the French "digérer," to digest. Digestifs range widely in strength, roughly 16% to 40% ABV, and are usually served in small pours, in a snifter or liqueur glass, to be sipped slowly.
Common styles include Italian amaro (bitter herbal liqueurs such as Campari, Averna, and Fernet-Branca), Cognac and Armagnac (French grape brandies), grappa (Italian grape spirit), limoncello (Italian lemon liqueur), ouzo (Greek anise spirit), and peppermint schnapps.
The claim that digestifs measurably aid digestion isn't well established scientifically; their better-documented role is as a traditional, unhurried way to close out a meal.