By the year 1000, the Mediterranean world was quite different from the Classical world. How and why did this happen?

Perhaps the most dramatic factor that changed the Mediterranean by the year 1000 CE was the rise of Christianity and Islam. The diverse religious beliefs of antiquity were largely replaced by two major monotheistic religions with orthodoxy of belief (rather than just token offerings) enforced by the government. Consequently, vast areas became united in their beliefs. Two factors accounting for the success of these religions in the Mediterranean were (1) their promise of an idyllic afterlife for their followers and (2) their usefulness in supporting imperial ideology.
Next, the capital of the Roman Empire shifted east from Rome to Constantinople, signaling an increasing division, both religious and linguistic, between the Greek east and Latin west. Part of this division grew due to barbarian invasions and conquests of territory that had been subject to Roman rule in antiquity.
Finally, in the chaos following the fall of the western Roman Empire, many smaller states arose that were organized along feudal lines.