The aftertaste of something was the taste it left behind after having been consumed already, which lingered long in the mouth. One particular coffee that President Vargeld enjoyed was slightly bitter, with a smoky aftertaste. He found it was "the best he had ever tasted". (PROSE: The Fall of Yquatine)
"Aftertaste" could also be used as a metaphor, and so one could experience the aftertaste of "enforced passivity", as experienced in travel, (PROSE: Qualia) or still have the lingering aftertaste of a dream. (PROSE: Verdigris)