The Great Schism is also known as the the Schism of 1054. It has also been called the East-West Schism.
The schism is unique because it is not a breakup of a country or government over political views. The great schism is the break between the Western Catholic church and the Eastern Orthodox church. The Western church, at the time, was led by Pop Leo IX, and the Eastern church was led by the Patriarch of Constantinople, Michael Cerularius.
There had been friction between the east and west churches for years, but 1054 is when everything finally fell apart. That was the year that the Pope decided to excommunicate the Patriarch. In retaliation the Patriarch excommunicated the Pope.
The friction between the east and west churches was more than just two guys who didn't like each other. It was focused on their interpretation of scripture and what to do with a few of the holy sacraments. There was disagreement on the interpretation of the Holy Spirit. There was disagreement about clerical celibacy, bishops' rights, and the use of unleavened bread for communion.
Rather than reconcile their differences, the church simply split into two sections: Eastern and Western. Both believed in the same God and his son Jesus Christ, but differed on religious practices.