Acedia comes from a combination of the negative prefix a- and the Greek noun kēdos, meaning "care, concern, or grief." (The Greek word akēdeia became acedia in Late Latin, and that spelling was retained in English.) Acedia initially referred specifically to the "deadly sin" of sloth. It first appeared in print in English in 1607 describing ceremonies which could induce this sin in ministers and pastors, but that sense is now rare. Acedia now tends to be used more generally to simply imply a lack of interest or caring, although it sometimes still carries overtones of laziness.
1607, in the meaning defined above
borrowed from Medieval Latin acēdia "apathy, torpor, sloth," borrowed from Late Greek akēdía "negligence, apathy," going back to Greek akḗdeia "carelessness, indifference," noun derivative of akēdḗs "uncared for, without care or worry, careless, heedless," from a- a- entry 2 + -kēdēs, adjective derivative of kêdos "care, anxiety, grief" — more at hate entry 1