French, literally "before," in various terms borrowed into English; cognate with Italian avanti, both from Late Latin abante, a compound of ab "from" (see ab-) and ante "before, in front of" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before") which meant "from in front of," but in Vulgar Latin came to mean simply "before."
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-).
The meaning "that which holds two or more things firmly together" (on the notion of clasping arms) is from mid-15c. Hence the word is applied to various devices for fastening and tightening. The 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."