The label of "New Literatures" includes the literary productions of a geographically and culturally vast and non-contiguous area that includes the former British colonies (for example, from Canada to Australia, from Singapore to Pakistant and India). Some critics debate whether or not to include the USA in this area, although their independence from Britain in the eighteenth century and the position of world power that hey have enjoyed have led many to exclude them. Yet, the case is often made for minority groups within the US (African-Americans, Latinos, Asians and other hyphenated groups) to be included in the New Literatures group. In addition to writers living in the formers colonies or writers of the past living under the colonial regime, authors uprooted from their native land because of colonialism such as Rushdie are also included in this group. The point of these introductory remarks is to make you aware that, although used as an umbrella term, "New Literatures" (significantly in the plural) incorporates very different literary products, each with its own cultural and geographical specificity. I think it is important to be aware of this specificity as it was long denied by the colonialist project which denied different identities.
Because of this denial, the search for a meaningful identity and a local cultural specificity to oppose to the cutlural assimilation of colonial rule or contemporary globalization is an important theme of New Literatures. This search for identity has been particularly meaningful for writers coming from minority groups such as women and queers. Their challenging of the established norms is to be seen as a fight against patriarchy/heteronormativity and colonialism (or its contemporary legacy in the globalization process) at the same time (see the works by Shyam Selvadurai and Arundhati Roy).
While New Literature usually refers to modern experiments in style, narrative techniques, linguistic experimentation, etc. (the means of telling a story rather than the content of the fiction itself), as in Faulkner, Joyce, the existential writers, and similar literatures, certain thematic trends can be discerned as well, reflected in the narrative and linguistic experimentation. Among them are the relation of selfhood vs. membership in a society; the balance of history and future prospects; the inner dialogue of the mind of the characters vs. the linguistic speech-acts of the characters; and of course, the rewards and dangers of moving away from tradition toward individualization (perhaps the most telling theme). These themes mark a new function for literature—not merely a fictionalizing, story-telling function, but a social challenge to rethink the world around us from time to time. New literature joined a larger modern art movement to look at things carefully, to give lesser importance to the past.
Since most of such literature exists today in ex or former British colonies ('Anglophone' literature/s), some chief/major thematic concerns (amongst many) include
1. Post-colonial/post-independence problems of these societies including political, social, economic and other problms
2. Issues of identity, selfhood, and the 'place' of many such nation and people in today's world
3. Contemporary 'angst' and various existential dilemmas in clash or contrast with traditional ways of life and customs and such challenges that are created by modernity
This is only a brief mention, Im sure that with more detaile research and reading into various texts in international English literature, you can come up with further points/factors.