Origins
An embrace is, at its most literal, an arm-wrapping. The word comes from Old French embracier — 'to clasp in the arms' — composed of en- ('in') and brace ('the two arms'). The brace descends from Latin bracchium ('arm'), itself borrowed from Greek brakhíōn ('upper arm').
The physical gesture is embedded in the etymology: to embrace someone is to take them inside your arms. The metaphorical extension — embracing an idea, a faith, a cause — arrived quickly. By the 15th century, English speakers were embracing concepts as well as people, and the arm-wrapping image gave the metaphor its warmth.
Latin bracchium fathered a family of arm-related words. A bracelet is an ornament for the arm. A brace is a support — originally something held up by arms. A bracket was a projecting support shaped like a bent arm, and only later became the punctuation mark.