There is significantly more than just one answer to your question. Just to give you a few examples, in my English degree post-colonial meant the literature of Canada, Australia, India, and other former colonial states, including the many post-colonial countries in Africa. The challenge is that these regions/nations may have significantly different responses to their former colonial states - post-colonial literature tends to wrestle with the impacts of the colonial past, and the ongoing impact of that past in the present.

It doesn't take much to see that an immigrant population in a nation like Canada or Australia is going to have a significantly different body of responses to this history than a state such as India or Uganda, where those doing the reflection have a history of being invaded rather than a history of emigration.

Within Canada for example, indigenous authors and thinkers by and large don't use the term postcolonial as we don't consider Canada to be "post" colonial but rather to still be a colonial power in every meaningful way, and instead we talk about things like decolonization (directly addressing colonial narratives and structures and either deconstructing or co-opting them) combined with other movements like resurgence (the re-affirmation of our own narratives, ways of engaging with the world and each other, rather than trying to carve out for ourselves a piece of a tasteless pie we wish didn't exist).

In some respects this gets to one of my personal biggest challenges with the idea of post-colonialism; few if any post-colonial governments have rejected colonialism - rather they have simply replaced a colonial administration with local leadership, but kept the same colonial system, the same hierarchical systems, and so on. This is especially true with transplanted colonial systems like Canada. As a result, for many administrations, a term like "post-colonialism" becomes simply a justification of their own power, or a way to avoid or deflect unwanted questions, something we saw from people like Gadafi or Mugabe, or from states like Russia who use similar rhetoric and finger pointing in trying to deflect from its own form of colonialism.

As to the specific ideas, it's hard! In part because as soon as you start making generalizations, exceptions start to show up. Many authors focus on legitimization their own voice, either in local languages or through the former colonizing langauge. Almost all post-colonial projects have in their heart the legitimization of a new identity that is separate from the roles allowed within the previous structure - but again, like I talked about above, those identities might still be colonial! Really, it might be best to just think of it as a process of identity genesis on a national scale, but usually still within the bounds of westfalian ideas of states, and often but not always more concerned with the legitimization of a new voice than of the rejection of colonial perspectives or even systems.