From Middle High German *ūfhœren*, a compound of *auf* ("up, off") and *hören* ("to hear, to heed"). The sense evolved from "to stop paying attention" to the general meaning of ceasing any activity. The separable prefix *auf-* here carries the force of completion or termination — a pattern shared with many German verbs (cf. *aufmachen*, *aufgeben*).

Germans use *aufhören* in a wide range of registers, from children being told *Hör auf!* ("Stop it!") to formal announcements. Note that *aufhören* is intransitive and must be followed by *zu* + infinitive when a specific activity is mentioned (e.g., *aufhören zu rauchen* — "to stop smoking"), unlike English "stop + -ing". Confusingly, *anhören* (to listen to) looks similar but means the opposite in feel — don't mix them up!