How did the Great Schism contribute to the Reformation?
I take vigorous exception to the response above. The Great Schism had no bearing whatsoever on the Reformation, and should not be regarded as such.
Assuming for the sake of argument that the Great Schism was the schism created by the Babylonian Captivity when the Popes were resident in Avignon (rather than the Schism normally denominated the "Great" Schism of 1054) the schism itself was ended by the Council of Constance of 1414, almost forty years before Luther issued his Ninety Five Theses. Although the papacy may have been politically injured, it did not lose prestige or authority within the Church itself.
Luther's disagreement with the Church resulted from an intense personal struggle over his concept of sin. His conclusion that salvation came from faith alone and that the Pope had no power in heaven came from his own personal reflection. Luther received support from a number of German princes who embraced his ideas because it would free them from the authority of the Holy Roman Emperor, not the Pope himself. It is important to note that it was the POLITICAL element of the Reformation, that is the German Princes wishing to be freed from the Emperor, that accorded Luther success. Religious authority was not a matter they considered. Although the Pope understandably opposed Luther's movement, Luther's dispute had no bearing whatsoever to the schism which had long since been healed. Granted their were intense problems within the church; absenteeism, clergy who did not abide by their vow of celibacy, selling of indulgences (to which Luther did object) but none of these was a result of or in any way related to the schism.
If the questioner refers to the true Great Schism of 1054 which separated the Eastern and Western Churches, and which remain separated to this day, then the argument above is even more specious.
I assume that you are talking about the schism that is known as the Western Schism, not the one that is known as the East-West Schism. Both of these are known as the "Great Schism" but only the former has much to do with the Reformation.
In the Western Schism, the Catholic Church split and there were, for a time, two competing popes. During this time, there was a man in Rome claiming to be the true pope and another in Avignon, France, claiming the same. This state of affairs lasted about 40 years, ending in 1417.
During the Reformation, one of the major critiques of the Catholic Church was that it gave too much power to the pope. Men like Luther argued that popes were not infallible and should not have as much power as they had. This argument was clearly helped by the experience of the Great Schism. If there could be two people both claiming to be pope, how sacred could the office be? The fact that there had been two (or even more) popes for such long periods of time lessened the prestige of the papacy in the eyes of the people and helped create support for the Protestant Reformation.