What do Orthodox Christians mean when they talk about the Real Presence in the Eucharist? The Orthodox Church is one of several denominations that teach the Real Presence, but they don't all have the same understanding of this doctrine. What is the Orthodox understanding?
We Eastern Orthodox take Christ at His word that "if you do not eat My Flesh and drink My Blood, you have no life in you." Indeed this is a hard saying---who can accept it? In my limited understanding as a babe in Orthodoxy (I entered the Orthodox Church but a year ago), we just accept it as a holy Mystery and try not to qualify it in philosophical terms. From my limited understanding and knowledge of Roman Catholic doctrine, this distinguishes our dogmatic approach towards the Holy Mysteries from theirs. However, I think the Eucharist is a mystical experience for both of us.

First and foremost, the Body and Blood of our Lord Jesus are not objects to be understood cataphatically or apophatically, but instead they are our food, and God Himself in us. They are primarily to be experienced (insofar as one experiences food), and only secondarily to be understood.