Old English dran, dræn "male honeybee," from Proto-Germanic *dran- (cf. Middle Dutch drane; Old High German treno; German Drohne, which is from Middle Low German drone), probably imitative; given a figurative sense of "idler, lazy worker" (male bees make no honey) 1520s. Meaning "pilotless aircraft" is from 1946.
Meaning "deep, continuous humming sound" is early 16c., apparently imitative (cf. threnody). The verb in the sound sense is early 16c.; it often is the characteristic sound of airplane engines. Related: Droned; droning.