A digestif (Cognac, Armagnac, Calvados, eau-de-vie, etc), as the name implies, may help you digest, but it is also designed to reinvigorate you after a meal and leave a nice taste in your mouth after your coffee (it’s also known as a pousse-café or la rincette). Some say it should be served in the still-warm coffee cup to bring out the liqueur’s aromas.
In the Middle Ages, the digestif of choice was Hypocras,
Ideally it should be served in your salon or garden, and is a hint to the guests that they should think about going home.
Image by Cocktailmarlerderivative work: Jocian