When we speak of the Great Schism, we can actually be referring to one of two schisms. The first is also called the East-West Schism and happened in 1054 when the Byzantine Church broke from the Roman Catholic Church. The second is also referred to as the Great Western Schism and happened between 1378 and 1417 when a pope in Rome and a second pope in Avignon, France, proclaimed themselves to be the real pope. Both schisms significantly affected the Roman Catholic Church. Though, typically, that which is called the Great Schism refers to the East-West Schism.
The greatest effect of the East-West Schism was the creation of two separate churches that had previously been unified under one church, the Eastern Orthodox Church and the Roman Catholic Church. But more specifically, the schism had developed over time due to "doctrinal, theological, linguistic, political, and geographic" differences; therefore, the schism also affected Catholicism by solidifying these differences (New World Encyclopedia, "Great Schism").
The greatest theological and political difference concerns the belief in the authority of the pope. The Roman Catholic Church holds that, as the successor of Saint Peter, the pope holds all authority over the Church. However, the Eastern Church feels the title of pope to be only an honorary one, so the church believes the pope has no authority to "determine policy" for all jurisdictions in the empire ("Great Schism").
A second significant theological difference concerns the objection of the insertion of the filioque clause in the Nicene Creed. The Nicene Creed is the statement of the Catholic Church's faith. The filioque clause refers to a specific statement of faith in the creed concerning the Holy Trinity; more specifically, the statement can be interpreted to mean that the Holy Spirit comes only from the Father or from both the Father and the Son. It is referred to as the filioque clause because the Latin word filioque translates to mean "and from the son." The Eastern Church changed their creed to read, "We believe in the Holy Spirit ... who proceeds from the Father," whereas the Roman Catholic creed reads, "We believe in the Holy Spirit ... who proceeds from the Father and the Son" ("Great Schism"; "Filioque Clause").