Hi there. The Orthodox view of atonement is almost unknown to all the people, but I will try to explain it here with some descriptions that I found on a page on the internet.
The Western view of atonement (Both Catholic and Protestant) is this: Substitutionary Atonement focuses on Christs suffering and death as the price for mans sin. In many ways, the model for Substitutionary Atonement is a courtroom. Due to his sin, man needed to be made right with a perfect and just God. Therefore, Christ came to suffer and pay the price in our place, i.e., He substituted Himself for us. Now, in the courtroom of God, those who accept Christ as their Lord and Savior are judged innocent. They have a forensic righteousness imputed upon them.
The Eastern view of atonement (Eastern Orthodox) is this: The Recapitulation Theory agrees that God needed to deal with mans sin. Man was separated from God as a result of the fall and, left to his own devices, was incapable of returning to God. However, Recapitulation sees the model through which God dealt with mans sin as a hospital rather than a courtroom. Instead of viewing the atonement as Christ paying the price for sin in order to satisfy a wrathful God, Recapitulation teaches that Christ became human to heal mankind by perfectly uniting the human nature to the Divine Nature in His person. Through the Incarnation, Christ took on human nature, becoming the Second Adam, and entered into every stage of humanity, from infancy to adulthood, uniting it to God. He then suffered death to enter Hades and destroy it. After three days, He resurrected and completed His task by destroying death.
To me, both sides make sense, but I find the EO view to be a lot more deeper and beautiful.