"Christ died for our sins in accordance with the scriptures" (1 Cor 15:3).
Our salvation flows from God's initiative of love for us, because "he loved us and sent his Son to be the expiation for our sins" (1 Jn 4:10). "God was in Christ reconciling the world to himself" (2 Cor 5:19).
Jesus freely offered himself for our salvation. Beforehand, during the Last Supper, he both symbolized this offering and made it really present: "This is my body which is given for you" (Lk 22:19).
The redemption won by Christ consists in this, that he came "to give his life as a ransom for many" (Mt 20:28), that is, he "loved [his own] to the end" (fn 13:1), so that they might be "ransomed from the futile ways inherited from [their] fathers"(1 Pet 1:18).
By his loving obedience to the Father, "unto death, even death on a cross" (Phil 2:8), Jesus fulfills the atoning mission (cf. Isa 53:10) of the suffering Servant, who will "make many righteous; and he shall bear their iniquities" (Isa 53:11; cf. Rom 5:19).
- Paras 619 to 623 of The Catechism of the Catholic Church
For a fuller explanation of this mystery, go to this commentary on the Summa Theologica of St Thomas Aquinas.