As Choy said, we believe that the Eucharist, in the Liturgy, becomes truly the Body and Blood of Jesus Christ, but there isn't really any more scholastic or scientific analysis beyond this. It has been what the Church taught from the beginning. Our Lord times tells us this very plainly:
"I am the living bread which came down from heaven: if any man eat of this bread, he shall live for ever: and the bread that I will give is my flesh, which I will give for the life of the world. The Jews therefore strove among themselves, saying, How can this man give us his flesh to eat? Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. For my flesh is meat indeed, and my blood is drink indeed. He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him. As the living Father hath sent me, and I live by the Father: so he that eateth me, even he shall live by me. This is that bread which came down from heaven: not as your fathers did eat manna, and are dead: he that eateth of this bread shall live for ever." (John 6: 51-58)
St. Paul affirms the very real meaning of this, saying:
"The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ? For we being many are one bread, and one body: for we are all partakers of that one bread." (1 Corinthians 10:16-17)
He then explains the severity of not considering seriously the Eucharist, and says that many are ill and dead (i.e., "sleep") because they profane the Body and Blood of Christ:
"For I have received of the Lord that which also I delivered unto you, that the Lord Jesus the same night in which he was betrayed took bread: And when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me. After the same manner also he took the cup, when he had supped, saying, this cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me. For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come.
Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. But let a man examine himself, and so let him eat of that bread, and drink of that cup. For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body. For this cause many are weak and sickly among you, and many sleep." (1 Corinthians 11:23-30)
We believe this passages of Scripture, as they are understood in the ancient Holy Tradition of the Church, and confess that the Eucharist is truly the Body and Blood. As I said above, however, Transubstantation is a particularly scholastic belief concerning that, which is dogma in the Roman Catholic Church. It is not dogma in the Orthodox Church.