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.