The Great Exchange
On Calvary there transpired the momentous and grandest transaction of all time and eternity. Christ the Substitute of his people (Isaiah 53) was laden with our guilt and trespasses just as if he himself had committed those sins: He was counted with the transgressors. “He hath made him who knew no sin to be sin for us, that we might become the righteousness of God in him” (2 Corinthians 5:21).
Christ took full responsibility for the sins of his people and by his death he made atonement for them. As the scapegoat he took them away from us. He died the just for the unjust (1 Peter 3:18).
By the same token, his righteousness is counted as ours. "He has clothed us with the garments of salvation." In justification we stand before God, not having our own righteousness by the righteousness of Christ imputed to our account.
The exchange consisted in Christ giving us freely what is his (righteousness, holiness, perfect standing, full obedience to the Law, etc.) and took our debt upon himself. In order for God not to forsake us eternally, God forsook him ("My God, my God, what hast thou forsaken me?"). By his punishment we are made whole; by his stripes we are healed. The Lord laid on him the iniquity of us all.
Conversely, on the basis of Christ's atonement, God lays upon us white and spotless garments, bright and clean, procured for us freely by Christ.