One of the most significant events in the history of Christianity is the "Great Schism" between Eastern and Western Christendom, which occurred in 1054 CE.
The separation was not sudden. For centuries there had been significant religious, cultural, and political differences between the Eastern and Western churches.
Religiously, they had different views on topics such as the use of images (icons), the nature of the Holy Spirit, and the date on which Easter should be celebrated.
Culturally, the Greek East has always tended to be more philosophical, abstract and mystical in its thinking, whereas the Latin West tends toward a more pragmatic and legal-minded approach. (According to an old saying: "the Greeks built metaphysical systems; the Romans built roads.")
The political aspects of the split date back to the Emperor Constantine, who moved the capital of the Roman Empire from Rome to Constantinople. Upon his death, the empire was divided between his two sons, one of whom ruled the western half of the empire from Rome while the other ruled the eastern region from Constantinople.
These various factors finally came to a head in 1054, when Pope Leo IX excommunicated the patriarch of Constantinople (the leader of the Eastern church). In response, the patriarch anathematized (condemned) the Pope. The Christian church has been divided into West ("Roman Catholic") and East ("Greek Orthodox") ever since.