the lingering state of provoked anger: the exasperated, irritated mood that stays after something has stirred you up
This is a rare word. It appears only once in the New Testament (Ephesians 4:26) and only a handful of times in the Greek Old Testament, and it seems not to have existed in ordinary Greek before Jewish translators coined it. That background gives it a distinct feel. It is not the common word for anger, and choosing it signals something more specific than plain temper.
In its Old Testament home the word almost always describes Israel provoking God, usually through idol worship and broken covenant loyalty. There the stress falls on the provocation itself, the act or the thing that stirs God up, more than on the resulting feeling. By the time Paul uses it of a person in Ephesians, the weight has shifted toward the inward state: your provoked, exasperated condition, the sore mood that settles in and refuses to cool.
The single New Testament verse tells you not to let the sun go down on it. That is the whole point of the word choice. Ephesians already commands readers a few lines later to put away anger altogether, so this is not permission to stew. It names the aftermath that must be resolved before nightfall, the bitterness that, left overnight, becomes an opening for evil.
The most debated question is whether the word points to the cause of the anger (the offense that provoked you) or to the resulting angry state itself. Most scholarship leans toward the resulting state, but the older Old Testament pattern and a strong minority read it the other way, so both readings are live.