The Church on earth is the visible continuation of that body which Christ established, and which has a shared faith and whose members are in communion with one another. It has Bishops, priests, and deacons which guide it, and it upholds the Apostolic Faith and Tradition. It is One, Holy, Catholic, and Apostolic.
And actually, the treatise I linked to does define the Church, but you do have to read it. There is a lot more here: http://orthodoxinfo.com/inquirers/inq_church.aspx
“The Church on earth is the visible continuation of that body which Christ established, and which has a shared faith and whose members are in communion with one another. It has Bishops, priests, and deacons which guide it”
That much is true. (Local churches have elders and deacons. Bishops / Elders / Presbyters are all the same thing as described in the New Testament, and probably Pastor is as well. Nowhere is an office of “priest” found as the term applies generally to all believers as a nation of priests. Priests offer sacrifices which is applicable to all believers.)
To clarify your definition of “Church” though, do you think the church is made up of anything other than people?
“it upholds the Apostolic Faith and Tradition”
That is true to the extent of how the words are commonly used, but not in the sense it is purported to mean. There is no Apostolic faith or tradition that is not found within the scriptures. Peter specifically and explicitly stated his purpose for writing was to keep his doctrine in remembrance after his departure (i.e. death).
“It is One, Holy, Catholic, and Apostolic.”
One? Yes. It is a “body” made of body parts which require it to be one in order for those parts to form a body.
Holy? By virtue of Christ’s atonement, yes.
Catholic? Not as a brand name. But in the Biblical meaning that beyond the local manifestation of the church, there is a universal Church made up of mortal, imperfect believers on earth AND perfected believers in Heaven awaiting the redemption of their bodies (i.e. resurrection). Christ is the singular head of the body. (Only the Satanic beasts of the apocalypse have multiple heads.) And since the earthly and Heavenly church are One, there is no need for a second head on earth.
Apostolic? As I said before, believers today only exercise apostolic authority by proclaiming what the apostles recorded in scripture and by being obedient to the scriptures . There are certain requirements specified in the New Testament to qualify as an apostle: being witness of Christ’s resurrection, miraculous signs confirming their claim of apostleship, and being personally taught by Christ. There have been false claims of apostleship ever since the church began, and we are instructed to test such claims. These are the tests. No one today meets these qualifications. However, the church does have apostolic authority to consult in the writings of the apostles which are scripture.