Dispersion: (Greek, Diaspora) is the term which was used to mean those Jews who lived outside Palestine. After the disastrous Jewish War of AD66-73 and the Roman destruction of the Temple in AD 70, large numbers of Jews moved away from their traditional home, especially eastwards into Mesopotamia. But the process of ‘dispersion’ began long before that. At least since their exile in the 6th century BC Jews had settled around the Middle East and the eastern Mediterranean.
By New Testament times probably more Jews lived outside Palestine than in it. There were estimated to be a million Jews in Egypt alone. Alexandria, Jews made up such a significant proportion of the population that they formed a distinct political unit, living in their own areas of the city and maintaining their own culture and lifestyle.
Their distinctiveness, here and elsewhere, often led to strained relations with the non-Jewish population. Greek and Roman writers often speak despairingly of the Jews who lived among them but whom they did not understand, and anti-Jewish riots were not uncommon.
By the New Testament period most of the main cities had a Jewish colony, with its own synagogue (or at least a place for prayer. These expatriate Jewish communities were a natural first contact for Paul, as a Jew, and other Christian missionaries as they moved around the Mediterranean world.
Jews of the Dispersion are sometimes referred to as ‘Hellenistic Jews”, Hellenism – the wave of Greek culture and ideas which rolled over the Mediterranean world following the conquests of Alexander the Great – remained the dominant strand in the culture of the eastern part of the Roman Empire. The dispersed Jews, away from the more conservative atmosphere of Palestine, adapted more readily to the Greek way of life. They did not abandon their distinctive religion and culture and cease to be Jews, but they were more willing to learn from and enter into dialogue with Greek ideas.
Many of the later Jewish writings, particularly those from Alexandria are deeply influenced by Greek philosophy, and use language which would have been quite unfamiliar to Palestinian Jews. Apollos, the learned Jew from Alexandria, no doubt belonged to this school, before his gradual conversion to Christianity.

James 1:1