"form-fitting undergarment to support a woman's breasts," by 1902, a euphemistic borrowing in the garment trade, from French brassière "child's chemise; shoulder strap" (17c.), from Old French braciere "arm guard" (14c.), from bras "an arm," from Latin bracchium "an arm," from Greek brakhion "an arm" (see brachio-). The French word was used 18c. in the sense "woman's underbodice."
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Definitions of bra from WordNet
an undergarment worn by women to support their breasts;