This week is Holy Week, the week Christians commemorate the crucifixion and resurrection of Jesus. This week is central to the Christian faith, for according to the tenets of that faith, the events Holy Week celebrates are those which brought about the Atonement, humankind's reconciliation with God.
According to traditional Christianity, the Atonement was accomplished through the death of Jesus on the cross. The common phrase is "Jesus died for your sins." Over the centuries, Christian theologians have come up with a number of theories about how Jesus' death accomplished the Atonement. An ancient theory, out of favor today, says that God had to give Jesus to the devil as a ransom to reclaim sinful humanity (and that He then cheated the devil by resurrecting Jesus and bringing him back to Heaven). Another theory says that because human sin is a violation against the infinite God, it is an infinite offense which carries an infinite penalty that humanity cannot possibly pay; thus, only the death of a sinless man who is also the infinite God—Jesus— was sufficient to pay the penalty. Yet another theory says that the moral example of Jesus' perfect life and his death for the sake of love moves us to repent from our sins and reconcile ourselves with God.
The traditional Christian theories of the Atonement are many and varied (the list above doesn't cover them all), but every one I've seen has at least three things in common. First, they all assume that humanity has truly sinned and has thus separated from God—that's why we need Atonement. Second, they all assume that it was Jesus' crucifixion that accomplished the Atonement. Third, they all assume that Jesus was unique, the "only begotten" Son of God, and thus the Atonement was something that he and only he could accomplish—the Atonement is dependent upon Who he is. Even the theory of Jesus as moral example, at least in its classic form, assumes that Jesus could be such a perfect moral example because he is God incarnate, and God sent him to provide that moral example.
A Course in Miracles, however, gives us a radically new theory of Atonement that overturns all three of these assumptions. First, the Course claims that we never sinned against God; Atonement is the recognition of that fact, "the recognition that the separation never occurred" (T-6.II.10:7). Second, it claims that "the crucifixion did not establish the Atonement; the resurrection did" (T-3.I.1:2). This is a bold departure from Christianity. In Christianity, the crucifixion is where all the theological action is, as we see from the above theories; while Easter is the most important Christian holiday, the resurrection it celebrates is a theological afterthought. Nothing much is said about the resurrection beyond the idea that it was God's "yes" to Jesus, His confirmation of Jesus' unique divine status.
This leads directly to the third difference between traditional Christian theories of Atonement and that of the Course. In the Course, the Atonement is not dependent on Jesus having any unique status as God's Son, for in the Course we are all God's Sons. Rather, it is the final demonstration of Jesus as a teacher. (The Course's version of Jesus' role in the Atonement is thus most similar to the "moral example" theory above, though different from that theory in important respects as well.) In his earthly life, he taught that because we are eternally loved and cared for by God, we can be as carefree as the birds of the air and the lilies of the field. He taught that no matter how much we think we have sinned against God, He loves us as the father loved the prodigal son. He taught that because we are beloved of God, we can love everyone as He does—even our "enemies," even those who strike our cheek or steal our shirt or conscript us to carry a burden. In his crucifixion (according to the Course), he taught that even the death of the body cannot affect who we really are as beloved children of God, so we can love and forgive even those who try to destroy us.
The resurrection, then, was not proof of Jesus' unique divinity, but his teaching demonstration of a universal principle: Because we are all beloved Sons of God who have never truly sinned against our Father, our life is eternal. Nothing—not even the death of the body—an change the eternal fact that we are beloved of God, and have never left His tender embrace. This is Atonement, and this is what Jesus came to teach us:
The resurrection demonstrated that nothing can destroy truth. Good can withstand any form of evil, as light abolishes forms of darkness. The Atonement is therefore the perfect lesson. It is the final demonstration that all the other lessons I taught are true. (T-3.I.7:6-9)