In a very brief reply:
The Orthodox understand the fall as a two-fold problem: mortality/death and personal guilt/sin. Thus, for salvation to happen, the problem of death had to be addressed as well as the problem of personal guilt/sin.
Death had to be put to death. But only One who had Life in Himself, could put death to death. So Christ had to taken on human nature, and die bodily as a man, then, as God, resurrect that human nature bodily. Thus, since God put on human nature in a particular body (the man Jesus) he was at one time a singular Person but also in his human nature at one with humanity (though without personal sin). When he died bodily, he took on the curse of death for all of humanity, and when he was raised bodily he imparted life to all of humanity. In Orthodoxy, the Paschal imagery has Satan taking the "bait" of Christ's dead body, but being "slain" on the "hook" of Christ's divine immortality. The grave attempted to "devour" Christ in his body, but instead took into itself very Life itself and was destroyed from within.
Death has to be dealt with. That is why the Resurrection is so central to Orthodox belief. One might have one's sins forgiven, but still (theoretically) be subject to death through human nature. One is still then cut off from God who is nothing but Life. This is why infants, who have no personal sin, are baptized: so that the principle of death can be put to death in them.
Of course, it is perhaps easy to understand the need for personal guilt/sin to be dealt with. Just as Christ is the only one who could impart Life to us by dying in our place, so, too, he is the only one who can impart righteousness to us by taking on our sins and bearing our guilt. Only the innocent/righteous man could cancel the blameworthiness/sinfulness of us mortal creatures. And this is why adults are baptized: so that the principle of guilty can be washed away (and of course they need the remedy for mortality as well).
So, Christ, being man is homoousios with us, of one essence/nature with us. He shared in our mortality by dying in his humanity, he shared in our sin by blamelessly taking on our guilt. He shared this with all beings who have a like nature (human nature) with him. And by our participation in his death and sacrifice, he joins us with his divine nature/essence as well (by grace), since he is homoousios with the Father. Christ is the "bridge": of one nature with all human beings, and of one nature with the Father and the Spirit.