"pulpit or platform from which a speaker addresses an audience," 1540s, originally in an ancient Roman context, from Latin rostrum, the name of the platform stand for public speakers in the Forum in ancient Rome. It was decorated with the beaks of ships taken in the first naval victory of the Roman republic, over Antium, in 338 B.C.E., and the Latin word's older sense is "end of a ship's prow," literally "beak, muzzle, snout," originally "means of gnawing," an instrument noun from rodere "to gnaw" (see rodent).
The beaks were an ancient form of ram, a beam spiked with pointed iron for the purpose of sinking other vessels. For the form, compare claustrum "lock, bar," from claudere "to shut." The extended sense, in reference to any platform for public speaking, is attested by 1766.
The classical plural is rostra, though in English this is more common in the original "ship's beak" sense and -rums often is used in the secondary sense.