Sure, I'm not too surprised that you're not familiar with it, given that the West has become increasingly alienated from the original Christian teaching on the matter ever since Anselm of Canterbury and John Calvin invented the current Protestant understanding.
The Orthodox understanding of Christ's death and Resurrection (the two are always understood in one context) is multifaceted.
God didn't sacrifice His Son to Himself. Jesus' death was like a sting operation. He died to destroy Death from the inside, and to break its hold over mankind. He freed us from slavery to sin and death, and also redeemed all the dead who would accept Him--Adam and Eve, those who died in the Flood, the Israelites, you name it. Jesus' ransom wasn't paid to God (God isn't the one with the problem, we are) and He didn't pay it to the devil (why would God pay a ransom to the devil?), but He paid it to the reality of death itself, since it was death that we were in bondage to. In our icons of the Resurrection, you will see Jesus busting open the gates of Hades, pulling up Adam and Eve out of their graves. This is sort of a composite view of
Christus Victor and
Ransom theory.
A good illustration of this is to be found in the Paschal Sermon of St. John Chrysostom, recited yearly at the Matins service of Pascha:
Let no one weep for his iniquities, for pardon has shown forth from the grave. Let no one fear death, for the Saviors death has set us free. He that was held prisoner of it has annihilated it. By descending into Hell, He made Hell captive. He embittered it when it tasted of His flesh. And Isaiah, foretelling this, did cry: Hell, said he, was embittered, when it encountered Thee in the lower regions. It was embittered, for it was abolished. It was embittered, for it was mocked. It was embittered, for it was slain. It was embittered, for it was overthrown. It was embittered, for it was fettered in chains. It took a body, and met God face to face. It took earth, and encountered Heaven. It took that which was seen, and fell upon the unseen. O Death, where is your sting? O Hell, where is your victory? Christ is risen, and you are overthrown. Christ is risen, and the demons are fallen. Christ is risen, and the angels rejoice. Christ is risen, and life reigns. Christ is risen, and not one dead remains in the grave. For Christ, being risen from the dead, is become the first fruits of those who have fallen asleep. To Him be glory and dominion unto ages of ages. Amen.
Another vital part of the Orthodox understanding of Christ's Crucifixion is what is called
Recapitulation theory. This states that Jesus became man, lived and died to fully take on every aspect of our humanity--and so bring it back and redeem it to His Divinity, healing our humanity. His death on the Cross is the ultimate sharing in our human experience--we say that one of the Trinity suffered and died in the flesh. After Christ rose from the dead and broke the power of death over humanity, Jesus fully reconciled us to God, and reopened to us the gates of Paradise which had been closed since the Fall. Jesus made atonement between us and God--and atonement literally means at-one-ment. Being fully God and fully man, Jesus bridged the gap between us and God, the gap that is the result of sin. Jesus' very Incarnation, life, death and Resurrection were all acts of salvation.
The final part of Orthodox understanding in this area is what we call the
Moral Influence theory. This states that Jesus taught and died to actually teach us something. Jesus gave His teachings--and backed it up by example. His death on the Cross is a demonstration of His overwhelming love for mankind, in that He willingly died for us on the Cross.
Now, the two things that Shabir Ally successfully dismantles (and which we Orthodox condemn as being flat-out wrong at best, and heretical at worst) are
Satisfactionary atonement and
substitutionary atonement.
If you'd like, I can provide Scripture and logical defenses for all of what I posted about the Orthodox view, and explain the difference between the Orthodox and Calvinist Protestant views.