Originally, Diaspora literally meant a “scattering” of the people and referred to the early Greek populations that scattered to colonize other territories. In the classical sense, however, after the translation of the Old Testament into Greek, the term Diaspora has always been connected to the “scattering” of the Jewish people after their various forceful removals from the Levant and later from Spain.
In postcolonial theory, the people of the former colonies who were either brought as workers or immigrated to the Euro-American regions and who still maintain some degree of contact or affinity to their original cultures are considered part of their respective Diaspora communities. The works produced by the members of a diaspora group, thus, qualify as postcolonial writing of the diaspora.
Wikipedia has a very good entry on the term: Diaspora.