The Orthodox Church is the communion of local Churches, each gathered around its bishop at the Eucharist, which confess the faith of the Apostles and of the seven Ecumenical Councils and share one Eucharist throughout the world.
In the New Testament, the church is first of all the people of God gathered in a particular place: „the Church of God which is at Corinth“ (1Co 1:2). Each such church, gathered around its bishop with the presbyters, deacons and people, celebrates the Eucharist and is the whole catholic church made manifest in that place. As St Ignatius of Antioch wrote, „where the bishop appears, there let the people be, just as where Jesus Christ is, there is the catholic church.“
The Orthodox Church is the communion of all these local Churches. They are organized in regional bodies, some of them called patriarchates, such as Constantinople, Alexandria, Antioch, Jerusalem, Moscow, Serbia, Romania, Bulgaria and Georgia, and others called archdioceses or metropolias, such as Greece, Cyprus or the Orthodox Church in America. All of them confess the same Creed, celebrate the same Mysteries and commemorate one another by name in the Divine Liturgy. The Ecumenical Patriarch of Constantinople presides in honor, as first among equals, but he is not a universal ruler over the other Churches.
The Orthodox Church understands herself as the one, holy, catholic and apostolic Church of the Creed, in unbroken continuity with the Church of the Apostles, the Fathers and the Ecumenical Councils. She is officially called the „Orthodox Catholic Church“; the name „Eastern Orthodox“ distinguishes her from the Roman Catholic Church, from which she has been separated since the eleventh century.
Sources
Catechism, Q261, Q279, Q280a; Study: The Structure of the Orthodox Communion. Ignatius of Antioch, To the Smyrnaeans 8. See also the article "The Orthodox Church Worldwide."