means the act of inflicting harm or hurt on someone in return for a wrong they did to you.

from From Old French 'revengier,' itself built from Latin 're-' (back) plus 'vindicare' (to claim, avenge, set free) — the same 'vindicare' that gives us 'vindicate' and 'vengeance.' So tucked inside revenge is the old idea of laying claim to something owed, the way you'd reclaim property — only what's being reclaimed is a debt of injury. The word arrived in English in the late Middle Ages, already carrying that ledger-keeping flavor.