The handing of authority to another to act in one's place. Delegation transfers the doing and never the answering for it.
Latin delegatio (an assignment, delegation), from delegare (to send on a commission, entrust), from de- (down, away) + legare (to appoint by law, from lex, law); the handing of authority to another to act in one's place, transferring the doing while the answering for it stays put.
Latin lex, law, sits inside the root — a delegation was always a legal appointment, not a favor granted informally. What travels with that appointment is the doing alone; the law never lets the answering for it travel with it.