The wrath of God is our experience of the total incompatibility of unrepented sin before the holiness of God.
The unrepentant sinner cannot endure the presence, and the holiness of God.There is for such a one wailing and grinding of teeth, anger and even rage when confronted by the existence of God and the demands of His justice and holiness.
God’s wrath does not mean in some simplistic sense that God is “mad” as if being emotionally worked up to fury. God is not moody and unstable. God is not subject to temper tantrums like we are. Rather this, God is holy, and the unrepentant sinner cannot endure his holiness, but experiences it as wrath.