Katallagē appears 4 times in the NT (Romans 5:11; 11:15; 2 Corinthians 5:18, 19) and its verb katallassō (G2644) appears 6 times. The word comes from kata (thoroughly) + allassō (to change, exchange), meaning 'a thorough change' — specifically the change from a state of enmity to one of peace. In commercial Greek, it was used for exchanging currency or settling accounts. In the NT, it describes the fundamental change in the relationship between God and humanity that Christ effected.
Paul's theology of katallagē in 2 Corinthians 5:18-21 is one of the most compressed and powerful statements in all of Scripture: God reconciled the world to himself through Christ, not counting people's sins against them; God made Christ to be sin so that we might become the righteousness of God; and God has given believers the 'ministry of reconciliation.' The stunning claim is the direction of reconciliation: it is not humans who reconcile God to themselves but God who reconciles humans to himself. The problem was on the human side (sin and enmity), but the initiative was entirely God's. Reconciliation is the relational dimension of atonement — if justification restores legal standing, reconciliation restores personal relationship.