The term "Great Schism" normally refers to the great break in 1054 between eastern and western Christianity. This, obviously was a much bigger deal than some squabbling of popes. The schism left us with the main two oldest branches of Christianity, the Orthodox church and the Roman Catholic church. Both of which share a common history before this date, and are direct heirs of the ancient institutional church. Their differences are numerous, and can almost entirely be blamed on fights over political and religious power. Sure there are some doctrinal differences, but at the time they differed in degree of emphasis than of anything substantial. Of course since this time the Roman Catholic church has changed a good bit, while the Orthodox church has remained essentially the same.
The key centers of power at the time were Rome and Constantinople. Initially, Rome was the sole capital and this is important because the organization of the Christian church mirrored that of the empire. The church was divided into providences each with its head, called a Patriarch. Rome, since it was the capital was given prestige and called the "first among equals". Later, a dual capital system was created, and both Rome and Constantinople served as the dual capitals of the Roman Empire. In the ranking system at the time, this meant that Rome and Constantinople were equalized in status. Trouble started brewing with the decline of the western part of the empire. It was eventually over run and advanced to a post-civilized state. This help tip the balance in Constantinople's favor, as the single capital then shifted completely to the east. Eventually even Rome itself was over run.
What we were left with then, is a bunch of bruised egos and over ambitious church leaders. This is a recipe for religious conflict. Rome tried to assert itself as THE head, Constantinople resented this greatly, it wanted to be running the show. Then both sides started trying to rationalize the conflict and began nit picking at all kinds of theological issues. One which stood the test of time is called the Filioque. Literally, this is Latin for 'and the son', these three words (or one in Latin) are blamed by some over simplistic analysts as being the biggest cause of the schism. The Nicene creed, is the document in which this controversy centers around. Rome, decided it would add this one word to the line talking about the procession of the Holy Spirit. The line originally said that it proceeded from the father only, the pope said the son (Jesus) too.
Well, in 1054 people were fed up with each other, Constantinople was the capital of an empire, Rome was off in no mans land, living in a post-apocalyptic utopia world. They just couldn't see eye, they were on different planets, irrelevant to each other’s daily lives. So finally they split, what happened is that the heads of each church delivered mutual articles of excommunication. The rest is history.
Oh, and then on the way back from one of their failed crusades the Roman Catholics sacked and pillaged Constantinople for no reason whatsoever.
Now THAT'S history.