Who taught it?
Anselm (1033-1109) was the first notable Christian thinker to express this view in his work Cur Deus Homo? [Latin for Why the God-Man?]
What does it teach?
This view is similar to substitutionary atonement. It states that our sins are an affront to the honor or dignity of God. He held that Christ substituted to satisfy God’s honor being defiled. While substitutionary atonement deals with the judgment and wrath of God, satisfaction theory deals with God’s honor. This view states that Christ made restitution for our sin, mending what was broken and paying back what was taken. It is also notable because it does not involve Satan in the atonement—contra the ransom theory.
Anselm, who originated this view, lived under the feudal system—not Roman law. Under the feudal system, justice was considered an offense against the feudal lord. Thus Anselm was most likely influenced by his culture.
Which passages support it?
Anselm framed his version of substitution in the milieu in which he lived. Therefore, much of his concept of the atonement comes from his culture—not Scripture. Scripture doesn’t emphasize the dignity of honor of God, but the wrath of God.