Reconciliation of sinners with God through the Incarnation, sufferings, and death of Christ..
In early days Western writers held that Christ by His sufferings made a payment to Satan to have him relinquish his right to man.
Following Anselm, it is now usually held that Satan had no rights over man, but that Christ suffered because man by sin had incurred a debt to Divine justice and that this required a satisfaction that could be paid only by a God-Man Redeemer.
It is also held, in accordance with Abelard, that a full equivalent satisfaction such as was made by Christ's death was not absolutely necessary; therefore the Incarnation was an act of love, though not exclusively so.
New Catholic Dictionary