Post-modernism means what ever it is now that has come after modernism. We know that modernism is finished, but we are not sure what it is that we are in now. So there is no name that has any meaning, except to negate modernism and to come after it without knowing what it is we are doing now that is different. It has come to be associated with the nihilism of the Deconstructionist movement of Derrida and is also called Post-Structuralism for a while, because it came after the definite movement of the Structuralists following the lead of Levi-Strauss. It is also called Post-Foundationalism because no one believes that there are any foundations any more. It is also called Post-colonialism because it comes after the Colonial period when third world states were economically rather than politically controlled by the West. Sometimes it is associated with the age of the internet when the first interactive mass media was created. Sometimes it is associated with Globalization.
But here is the crucial issue which is that Continental Philosophy has been trying to end the Metaphysical Era for a long time, and Post-modernism is the sign we do not know whether it has ended yet. The metaphysical era started with Anaxamander and followed the Mythopoietic Era. Now we have been in the Metaphysical Era for a long time, even though its problems have become very clear, and so various philosophers have tried to put and end to it, without success and so modernism turns into post-modernism as we wait for the Metaphysical Era to put and end to itself. So all the Posts are just endless appendices as we wait for the other shoe to drop and to escape from the Metaphysical worldview. It is basically a philosophical version of Waiting for Godot.