The "Great" or "Eastern" Schism refers to a break in the communion between the Roman Catholic and Orthodox Churches in 1054. This was actually part of a long process that began in the sixth century, continued through the Photian Schism, and really was not finalized until the Council of Florence in 1439, in which the two churches gradually drew apart over differences concerning spheres of influence, theology, language, and liturgy.
The first major issue was the clash between the notion of papacy, in which the Bishop of Rome claimed to be the vicar of Christ on earth and have power over all other bishops as a "Pope," versus the eastern concepts of the "pentarchy" in which each bishop is responsible for his own diocese but the five patriarchs, bishops of the major cities of Rome, Jerusalem, Antioch, Constantinople, and Rome, are "primus inter pares."
Next, the Council of Toledo (in Spain) in 589 added the phrase "filioque" into the Nicene Creed. The Pope gradually approved a shift in the Roman liturgy to accept this phrase. The Eastern Church refused to accept that a local council and the Bishop of Rome (which they consider the proper title of the official the western church calls the Pope) had the right to unilaterally change a creed agreed upon by an ecumenical (universal) council. This led to a fundamental difference in which the Eastern Church argued that only ecumenical councils of the entire church can set forth authoritative statements about doctrine, while the western church argued that the Pope alone could do so.
One major effect that the schism had was that in response to it the Roman Catholic Church attempted to articulate and clarify many of its own doctrines. Secondly, the ambivalent relationship between the churches led to the Crusades having two opposed motives of saving and conquering Constantinople.