I'm not Orthodox, but I'll do my best here. And my Orthodox friends can correct me where I'm wrong.
In Orthodoxy there is a concept known as autocephelousy. Unlike, for example, the Roman Catholic Church where there is an idea of a universal bishop, an earthly head of the whole Church on earth (which Orthodoxy totally rejects as wrong); Orthodoxy instead believes that all bishops are full equals. Certain bishops are afforded certain honors, based on historical respect toward the historic jurisdiction; these include the ancient patriarchates of the Church. In antiquity there were five notable seats which were of high esteem, these were: Rome, Constantinople, Alexandria, Antioch, and Jerusalem. The bishops of these seats were known as patriarchs. This position of honor was not a position of de facto authority, these were positions of honor not authority; however because of that honor the bishops who held these seats were often given deference in some cases. Before the East-West split, for example, the bishop of Rome was highly honored and respected, because historically bishops of Rome were great defenders of Christian orthodoxy against heresy. But, again, it was never a greater position of authority; it was always a position of honor, of respect.
Since bishops are all equal, with no bishop having authority over the whole Church; but each bishop of his diocese and with certain dioceses being historically honored, as Orthodoxy existed in other places--such as spreading among the Slavic peoples for example--new autocephalous (self-ruling) churches were established. This led to, for example, a Patriarch of Moscow. And so there is a Russian Orthodox Church (the Orthodox Church in Russia) and a Greek Orthodox Church (the Orthodox Church in Greece). It is Russian because it is in Russia with a Russian patriarch; or Greek because it is in Greece with a Greek patriarch, etc. Not two different Churches, but one and the same Church in different geographical locations.
Not all Orthodox churches have been in continued communion, this is where the Chalcedon/non-Chalcedon split comes in. The Church in Egypt (the Coptic Orthodox Church) and the Church in Armenia (the Armenian Apostolic Church) are examples of non-Chalcedonian Orthodox Churches; while the Russian and Greek Orthodox are examples of Chalcedonian Orthodox Churches.
That said, in modern times, this old schism between the Chalcedonian and non-Chalcedonian Orthodox Churches is waning. Lots of dialogue has largely shown that the old schism was never really a theological disagreement, but a difference in semantics. And so the day is probably going to come when communion is restored.
But, in brief, there is only one Orthodox Church; but there are various autocephelous or self-ruling churches which are in communion together as that one Orthodox Church. Because the unity of the Church is in the common Orthodox faith, in the equal brotherhood of her bishops together. There is no "top dog" in the Orthodox Church, because the Church only has one Head, and that's Jesus Himself. Every bishop, and thus every parish, every diocese, every patriarchate is a temporal jurisdiction of Christ's one and only Church throughout the whole world.
-CryptoLutheran