early 15c., drom, "percussive musical instrument consisting of a hollow wooden or metallic body and a tightly stretched head of membrane," probably from Middle Dutch tromme "drum," a common Germanic word (compare German Trommel, Danish tromme, Swedish trumma) and probably imitative of the sound of one.
Not common before 1570s; the slightly older, and more common at first, word was drumslade, apparently from Dutch or Low German trommelslag "drum-beat," "though it does not appear how this name of the action came to be applied to the instrument" [OED], and the English word might be a shortening of this. Other earlier words for it were tabour (c. 1300, ultimately from Persian; see tabor) and timpan (Old English; see tympanum).
In machinery, the word was applied to various contrivances resembling a drum from 1740. In anatomy, "the tympanum of the ear," 1610s. Meaning "receptacle having the form of a drum" is by 1812. Drum-major (1590s) originally was "chief or first drummer of a military regiment;" later "one who directs the evolutions of a marching corps."
"beat or play time on, or announce by beating on, a drum," 1570s, from drum (n.). Meaning "to beat rhythmically or regularly" (with the fingers, etc.) is from 1580s. Meaning "force upon the attention by continual iteration" is by 1820. To drum (up) business, etc., is American English 1839, from the old way of drawing a crowd or attracting recruits. To drum (someone) out "expel formally and march out by the beat of a drum" is originally military, by 1766.