mid-14c., "sea nymph who by her singing lures sailors to their destruction," from Old French sereine (12c., Modern French sirène) and directly from Latin Siren (Late Latin Sirena), from Greek Seiren ["Odyssey," xii.39 ff.], one of the Seirenes, mythical sisters who enticed sailors to their deaths with their songs, also in Greek "a deceitful woman," perhaps literally "binder, entangler," from seira "cord, rope."
Meaning "device that makes a warning sound" (on an ambulance, etc.) first recorded 1879, in reference to steamboats, perhaps from similar use of the French word. Figurative sense of "one who sings sweetly and charms" is recorded from 1580s. The classical descriptions of them were mangled in medieval translations and glosses, resulting in odd notions of what they looked like.