What does 'vengeance is mine' mean in relation to Christ's sacrifice?

The phrase 'vengeance is mine' underscores the truth that God holds ultimate authority over justice and judgment. In His perfect holiness, God cannot overlook sin; it must be punished. However, through Christ's sacrifice, God executed His vengeance upon sin by placing it on His Son. Hebrews 10:30 emphasizes that God will judge His people, but for those in Christ, this judgment has already been satisfied by His death on the cross. Thus, believers need not fear God's wrath, as Christ bore it in their place, fulfilling divine justice while allowing them to walk in grace and forgiveness.