What was the significance of the Byzantine Empire to Western Europe?
The Byzantine Empire represented the last stronghold of Christianity in the East. Unlike the Western Roman Empire which fell in 476 CE, the Byzantines did not fall until 1453 at the hands of the Seljuk Turks and Sultan Mehmet II. To the Medieval world, the Byzantines were the buffer of Christianity that separated them from the Muslim World, Mongols, and other invaders.
The Byzantine Empire also represented cultural heritage for the West—it was over the site of ancient Greek and Roman territory, and many ancient and classical artifacts were still alive within Constantinople.
Once the Byzantine Empire fell to the Ottomans in 1453, Christianity was in danger once more. Like the Battle of Tours in 732, when Charles "the Hammer" Martel defended Christianity in Europe from the Umayyad Caliphate creeping into Spain, Europeans felt that Islam was encroaching.
Specifically to trade, Europeans relied on the Christian Byzantine emperors to trade with the East and provide Europe with goods from the Silk Roads. Now that Constantinople fell and became Istanbul, Christian traders refused to do business with the Muslim city, citing higher prices and middleman costs. This encouraged explorers to build up their navigation techniques and find new trading routes to India, sparking the Age of Exploration.
The Byzantine Empire influenced the development of religion, culture, and politics in western Europe. On a religious level, the seven ecumenical councils of the Christian Church, all held before the eastern schism, were convened by emperors who ruled the eastern Greek (as opposed to western Latin) part of the Roman empire (Nicea, Chalcedon, etc. were all near Constantinople). The eastern concept of the `pentarchy` with co-equal bishops rather than a unique Pope became the model of Anglican and Lutheran ecclesiastical polity.
In culture, Greek learning and language were preserved in Byzantium after the fall of Rome in the 6th century. The tradition of ancient culture was preserved in the Byzantine and Arab worlds, and gradually transmitted back to the west from the twelfth through the sixteenth centuries, due to a combination of trade, crusades, and refugees.
Finally, the Crusades were launched in response to appeals from the Byzantine Empire for military help against Turks and Arabs.
Before 1453, Constantinople was the gateway to the Middle East for crusading armies. Byzantium was also important as a trading empire with the West, especially immediately after the fall of Rome. Byzantine pottery and metalwork was quite popular in Europe during the Middle Ages, and Byzantium was also important in the spice and silk trade with the East. Byzantine coins were regarded as very valuable with traders in Western Europe and the Middle East. Byzantine scholars also maintained studies in Greek and Roman philosophers who were considered to be pagans by the early medieval Church. This would be important during the Renaissance when Western Europe rediscovered the classics. Byzantium was also the strongest state in Christendom and may have saved Europe from being overrun by invaders from the Middle East.