A vengeful person badly wants to hurt someone back for something that person did to them. It describes not a single act but a state of mind — the wish for revenge, sitting inside someone, often for a long time. 'A vengeful ex-husband', 'she felt vengeful', 'a vengeful god'.

Two things make this word what it is. First, it is nearly always negative. English lets you feel that the wrong done to you was real, and still judge you for wanting revenge — 'vengeful' says you have gone too far, that the wanting has taken you over. If you want to say that punishing someone was fair, you use different words: just, deserved, fair. Second, it suggests something cold and patient. An angry person shouts and it passes; a vengeful person waits. That is why it fits so well with stories — vengeful ghosts, vengeful spirits, vengeful villains are everywhere in films and novels, and this is where students most often meet the word.

The related noun is 'revenge' (much more common than the older noun 'vengeance', which sounds biblical or dramatic — 'vengeance is mine'). Everyday English prefers 'take revenge on someone' or 'get back at someone'. Keep 'vengeful' for the adjective, describing the person or their feeling: 'He isn't a vengeful man'.