A digestif (Cognac, Armagnac, Calvados, eau-de-vie, etc) as the name implies may help you digest but it is also designed to leave a nice taste in your mouth at the end of dinner after your coffee (it’s also known as a pousse-café). Some say should be served in the still-warm coffee cup to bring out the liqueur’s aromas.
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