"shallow, flat vessel containing hot water in which another vessel is placed to heat its contents gently," by 1733 (in a cookery book, earlier, 1724 as the name of a meat dish cooked in one), from French bain-marie, from Medieval Latin balneum Mariae, literally "bath of Mary."
According to French sources, perhaps so called for the gentleness of its heating; others credit the name to the supposed inventor, Mary the Jewess, mentioned in early gnostic writings and looked on since 4c. C.E. as a founder of alchemy. Middle English had balne of mary (late 15c.). French bain was used by itself in English in various sense 15c.-17c.; it is from baigner "to bathe" (12c.), from Latin balneare, from balneum "bath" (see balneal).