I can't add much to Aristibule's explanation. However, if you ever are able to go to a Divine Liturgy (whether that of St. John Chrysostom or St. Basil or, very rarely, St. James) you will notice that after the words of institution (what the Romans call the Canon of the Mass), the priest will say the following:
We offer to Thee this reasonable and unbloody sacrifice;
and we beg Thee, we ask Thee, we pray Thee that Thou,
sending forth Thy Holy Spirit on us and on these present gifts"
(the Deacon says: "Bless, Lord, the holy bread")
"make this bread the Precious Body of Thy Christ"
(Deacon: "Amen. Bless, Lord, the holy chalice"):
"and that which is in this chalice, the Precious Blood of Thy Christ"
(Deacon: "Amen. Bless, Lord, both"),
"changing by Thy Holy Spirit"
(Deacon: "Amen, Amen, Amen.") This is what we refer to as the
epiklesis which refers to the descent of the Holy Spirit upon the gifts so that they become the body and blood of our Lord and Saviour, Jesus Christ. Although the old Roman Canon does not necessarily have an explicit
epiklesis, this has been enough of a dividing issue that even Western Rite Orthodox who essentially use the Roman Rite (in use before the Novus Ordo or even the Tridentine Rite) have a Byzantine Rite
epiklesis in their liturgies because, apparently, St. Tikhon, Patriarch of Moscow, who adapted the Western Rite for official use in the Russian Diaspora, thought there was one lacking. This also brings up other issues between the RC and the EO. Do the EO believe in
transubstantio? The use of the
epiklesis seems to indicate that we do. In fact, in the
Confession of Dositheus the Latin term
transubstantio is represented by the Greek
metamorphosis which are calques of one another. The EO do not subscribe to the logical suppositions of the Latin term, i.e. arguing whether the presence of Christ subsists under the elements of bread and wine. Unfortunately, many people would be simplistic and say that the EO and the RC believe in the same thing, when this is not the case. For this reflects much about our understanding of the Eucharist, which is referred to as the "Mysteries" or "Mystical Supper." Whichever one you choose, it reinforces the EO belief that what is given to us supersedes any attempt to explain what it is. We can be sure that it grants us forgiveness of sins and life eternal, but we do not now the how or the what.
I'm sorry if I have confused you (believe me, I am too

).