The Collaborative International Dictionary of English v.0.48:

Eastern Church \Eastern Church\
   That portion of the Christian church which prevails in the
   countries once comprised in the Eastern Roman Empire and the
   countries converted to Christianity by missionaries from
   them. Its full official title is The Orthodox Catholic
   Apostolic Eastern Church. It became estranged from the
   Western, or Roman, Church over the question of papal
   supremacy and the doctrine of the filioque, and a separation,
   begun in the latter part of the 9th century, became final in
   1054. The Eastern Church consists of twelve (thirteen if the
   Bulgarian Church be included) mutually independent churches
   (including among these the Hellenic Church, or Church of
   Greece, and the Russian Church), using the vernacular (or
   some ancient form of it) in divine service and varying in
   many points of detail, but standing in full communion with
   each other and united as equals in a great federation. The
   highest five authorities are the patriarch of Constantinople,
   or ecumenical patriarch (whose position is not one of
   supremacy, but of precedence), the patriarch of Alexandria,
   the patriarch of Jerusalem, the patriarch of Antioch, and the
   Holy Synod of Russia. The Eastern Church accepts the first
   seven ecumenical councils (and is hence styled only
   schismatic, not heretical, by the Roman Catholic Church), has
   as its creed the Niceno-Constantinopolitan (without the later
   addition of the filioque, which, with the doctrine it
   represents, the church decisively rejects), baptizes infants
   with trine immersion, makes confirmation follow immediately
   upon baptism, administers the Communion in both kinds (using
   leavened bread) and to infants as well as adults, permits its
   secular clergy to marry before ordination and to keep their
   wives afterward, but not to marry a second time, selects its
   bishops from the monastic clergy only, recognizes the offices
   of bishop, priest, and deacon as the three necessary degrees
   of orders, venerates relics and icons, and has an elaborate
   ritual. See also Greek Church, under Greek.
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

Eastern Church
    n 1: derived from the Byzantine Church and adhering to Byzantine
         rites [syn: Orthodox Church, Orthodox Catholic Church,
         Eastern Orthodox Church, Eastern Church, Eastern
         Orthodox]
    2: the Catholic Church as it existed in the Byzantine Empire
       [syn: Eastern Church, Byzantine Church]