early 14c., "piece of armor for the arms," also "thong, strap for fastening," from Old French brace "arms," also "length measured by two arms" (12c., Modern French bras "arm, power;" brasse "fathom, armful, breaststroke"), from Latin bracchia, plural of bracchium "an arm, a forearm," from Greek brakhion "an arm" (see brachio-).
Meaning "that which holds two or more things firmly together" (on notion of clasping arms) is from mid-15c. Hence applied to various devices for fastening and tightening. Meaning "a prop, support," especially in architecture, is from 1520s. Of dogs, ducks, pistols, etc., "a couple, a pair" from c. 1400. Braces is from 1798 as "straps passing over the shoulders to hold up the trousers;" from 1945 as "wires for straightening the teeth."