What effect did the Great Schism have on Catholicism?

Answer

It shook the foundation of the religion, which held that the one true pope was the ultimate authority on religious matters.  

Answer

The Great Schism occurred in 1054, when the major Christian Church split into what became known as a Catholic Church in the west and Orthodox Churches in the east. This split was triggered by disagreement over the exact nature of the Holy Trinity, as well as the ordination of married priests. Although these were the nominal reasons for the split, underlying friction had been brewing for centuries, with the bishop of Rome claiming to be more than merely equal to the other Metropolitans and even holding the right to proclaim doctrine without their consent.

The Great Schism freed the Catholic Church of all remaining constraints of the eastern patriarchs, and no longer needed to consider their views on matters of faith. It was now able to define the pope as the leader of the Church and God's representative on earth. Over time, more powers were accorded to the pope until, by 1870, he was considered infallible when speaking ex cathedra on matters of faith.

The Western Schism was a much later and less significant event, in which claimants to the Catholic papacy squabbled over their right to be pope.

Roman Catholic Answer
The Great Schism, otherwise known as the Western Schism is not to be confused with the Schism of the East. The Schism of the East was when the Eastern Church broke into two factions, half staying with Rome, and half formed what is now called the Orthodox Church. Many contemporary, particularly protestant scholars seem to confuse the two. What is called the Great Schism in the Catholic Church was the Western Schism, which, even more confusing, was not really a schism in the sense that the Schism of the East was, but a time when the Church had more than one claimant to the Papal Throne, finally resulted in three, one pope and two antipopes.
The effect that it had on Catholicism was immense, as it was one of the contributing factors to what would later become the protestant revolt, as it greatly weakened the papacy at a time when we were going to need a strong papacy to deal with the heresies arising with the "reformers".
from
Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

The Great Schism, otherwise known as the Western Schism, 1378-1417, when there was controversy over the true succession to the papacy. It began with the writings of Marsilius of Padua c. 1275- 1342), who claimed that a pope is subject to a council of bishops, priests, and laymen. Urban VI was elected Pope on April 8, 1378, following the seventy-year Avignon residence of the papacy. He was a stern reformer and also harsh. The French cardinals in retaliation declared that Urban had not been validly elected and proceeded to elect Robert of Geneva as the antipope Clement VII (1378-94). Clement withdrew to Avignon and the Great Schism was in full swing. France, Scotland, and Spain gave their allegiance to Clement; England, Italy, Flanders, Hungary, Poland, and most of Germany followed Urban, who died in 1389. There followed a succession of lawful popes at Rome and antipopes at Avignon. The universities of Paris, Oxford, and Prague disputed how the impasse should be resolved. Finally pope and antipope were invited to a council at Pisa (1409); both decline and were declared deposed by the council, which proceeded to elect yet another antipope, Alexander V (1409-10). In desperation, Emperor Sigismund of Germany appealed to the antipope John XXIII of Pisa, to call a general council at Constance, a German city on the Rhine. John agreed, and the council, later legitimized, was convened in 1414. It lasted four years and finally resolved the schism. The Pisan antipope John XXIII abdicated. Gregory XII, the true Roman Pontiff, having formally convoked the Council of Constance, sent his representatives, and then, for the good of the Church, freely resigned his office. The claim of Benedict XIII of Avignon was no longer worthy of serious consideration. The chair of Peter, vacant at last was filled by the election, November 11, 1417, of Pope Martin V. The Great Schism was ended.