In regards to Constantinople and the Byzantium time period, what was so important about it?
After the collapse of the Western Roman Empire, the Byzantine Empire was the sole remaining "Roman" Empire. Much of Roman tradition that was preserved had been preserved at Constantinople, the capital of Byzantium. Byzantine scholars had preserved a great deal of both Roman and Greek knowledge that was lost to the West. It also occupied a unique geographical location on the Golden Horn overlooking the Straits of Bosporus which made it easily defended. It was surrounded on three sides by water and on the land side by a wall so thick that a team of horses could be turned around on its surface. Constantinople also uniquely was situated where Eastern and Western merchants and caravans congregated. As a result, it became extremely wealthy as a trading city. It was the extreme wealth of Constantinople that tempted the Crusaders of the Fourh Crusade to sack it in 1204. It's importance as a trading city; is emphasized by the fact that only after it fell to the Turks in 1453 were serious attempts by Western Europeans made to circumvent that city and trade directly with the West.
Constantinople was so well known that its residents simply referred to it as Istimbolin, Greek for "in the city." This name was corrupted by the Turks to give the city its present name: Istanbul.