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.
The French cognate embrasser underwent a striking shift. In modern French, it primarily means 'to kiss' rather than 'to hug' — the gesture migrated from a full-body clasp to lip contact. Spanish abrazar preserved the original hugging sense. English embrace kept the arm-wrapping meaning but gained the abstract sense that French lost.
The word carries an emotional charge that 'hug' lacks. You hug a friend, but you embrace a cause. The extra syllables and the Latin ancestry give embrace a gravity that suits moments of commitment rather than casual affection.