Well, we all share the same beliefs, handed down to us by the Apostles, and our administrative unity comes through being in communion with one another...
In the case of the Eastern Orthodox Church:
Ecumenical Patriarchate of Constantinople
Orthodox Church of Alexandria
Orthodox Church of Antioch
Orthodox Church of Jerusalem
Orthodox Church of Russia
Orthodox Church of Serbia
Orthodox Church of Romania
Orthodox Church of Bulgaria
Orthodox Church of Georgia
Orthodox Church of Cyprus
Orthodox Church of Greece
Orthodox Church of Poland
Orthodox Church of Albania
Orthodox Church of the Czech lands and Slovakia
Orthodox Church in America
All churches are autocephalous (with the OCA being questioned by some), that is self-governing. Each has defined boundaries, each is governed by a Council of Bishops/Synod with it's Primate. That Primate holds the titles of either: Patriarch, Metropolitan or Archbishop.
However, the sole head of the entire Church is Christ himself.
The churches are in full communion with one another, reflecting a unity of faith and governance. We aren't governed by a single Bishop, though the "first among equals" is the Patriarch of Constantinople (currently His Grace, Patriarch Bartholomew) holds special position, he is not able to make a decision that supercedes or interferes in other churches. (unless the canons state that during a dispute, he must intervene)
This, as it is known, was the original position of the Latin Pope (Patriarch of Rome), however, in the 11th, 12th and 13th Centuries, the Latin Popes began to skew their position more and more and misunderstood their position in the Church. This was partially due to the barbarians and the "Holy" "Roman" "Empire", as well as other factors.
Decisions on important doctrine are decided by councils, which are held with Primates, Bishops, Clergy, etc... in attendance. Thus the decisions made at the Councils are universal across the church. Some Ecumenical Councils saw some churches missing during the discussions, but the decisions were just as universal and true for the whole Church. The wasn't one council where a Bishops declared that his decision was the law, with the other Bishops submitting to him. At all councils, the churches agreed together and the "first among equals" presided, but did NOT dictate nor decide for all of them.
The Orthodox Church is fully united in faith, doctrine, canons, law, administration etc...
I apologize in advance if any of this is incorrect. This is from what I remember from what I've been taught, as well as what I've read in various literature such as "The Orthodox Church" by Metropolitan Kallistos Ware