The Great Schism, also known as the Great Schism of 1054 or the East-West Schism, was the schism by which the Roman Catholic Church and the Eastern Orthodox Church separated. This was such a long-running argument that they excommunicated each other in 1054, and only ended the mutual anathema in 1965. Rome suppressed the use of Greek and the Orthodox suppressed Latin - setting scholarship back a long way especially in the Roman half. The result of the schism was that they were two separate churches by the time of the Crusades.
Use of Latin or Greek was part of a larger cultural difference. The east concerned itself more with art, mysticism and philosophy while the west was predominantly practical. Easterners sought union with God while westerners preoccupied themselves with sin and the price Jesus allegedly paid. The cross was the predominant religious symbol in the west while the resurrection was more important in the east. When western Crusaders plundered Constantinople in1204 reunion became impossible. There was large-scale killing and property destruction, religious sites were desecrated, the Orthodox east came to hate the Roman Catholic west.
Official reasons for the separation
The official theological disagreements between the two churches were on whether you should use leavened or unleavened bread for the Eucharist and whether the Holy Spirit proceeds from the Father or from the Father and the Son - something known as the Filioque. The reason for the argument about whether to use bread or wafers is that Roman Catholics are trying to recreate what was done at the Last Supper (and so use wafers that look nothing like normal unleavened bread) whereas the Orthodox are trying to recreate a communal meal so use bread.
The actual reason for the separation
Power and politics. As ever.
The Bishop of Rome thought he was the Pope. The Patriarch of Constantinople thought that it was a matter of first among equals and that only Constantinople and Rome of the historic five
seas sees were not under Muslim control so it should be the first two. And he wasn't going to play second fiddle to someone from a poor backwater (as Rome was at the time while Constantinople was the capital of the Roman Empire).