It is a large multidisciplinary movement encompassing advances in the arts, sciences and humanities. More to the point, there's probably not going to be a straightforward definition that isn't incredibly broad; it may be helpful to think of this term (as with 'analytic' and 'continental') as denoting a series of family resemblances among many different works of art, history, literature and philosophy.
All that being said, Frederic Jameson's Postmodernism, or the Cultural Logic of Late Capitalism might not be the worst place to start. Here is how he introduces the problem:
The last few years have been marked by an inverted millenarianism in which premonitions of the future, catastrophic or redemptive, have been replaced by senses of the end of this or that (the end of ideology, art, or social class; the “crisis” of Leninism, social democracy, or the welfare state, etc., etc.); taken together, all of these perhaps constitute what is increasingly called postmodernism.
You can read the first few sections of chapter one here.