Post Modernism can probably be best described as a critique of (or reaction to) modernism. Therefore to understand Post Modernism one has to be familiar with the concept of Modernism.
Modernism as an art form emerged in the mid-19th century, mainly in France, and was rooted in the idea that "traditional" forms of art had become outdated, and that it was therefore essential to sweep it aside. It was akin to previous revolutionary movements like liberalism and communism. Modernism encouraged the reconsideration of every aspect of existence, from commerce to philosophy, with the goal of finding that which was "holding back" progress, and replacing it with new, and therefore better, ways of reaching the same end. In essence, the modernist movement argued that the new realities of the industrial and mechanized age were permanent and imminent, and that people should adapt their worldview to accept that what was new was also good and beautiful.
Postmodernism, is very much like modernism in some aspects, it follows most of these same ideas, rejecting boundaries between high and low forms of art, rejecting rigid genre distinctions, emphasizing pastiche, parody, irony, and playfulness. Postmodern art (and thought) favors reflexivity and self-consciousness, fragmentation and discontinuity, ambiguity, simultaneity, and an emphasis on the destructured, decentered, dehumanized subject.
However, while postmodernism seems very much like modernism in these ways, is different from modernism in its approach towards this very ideas. Modernism, for example, tends to present a disillusioned view of human subjectivity and history (think of some cubist paintings) and presents that fragmentation as something tragic, something to be lamented and mourned as a loss. Many modernist works try to uphold the idea that works of art can provide the unity, coherence, and meaning which has been lost in most of modern life; art will do what other human institutions fail to do. Postmodernism, in contrast, doesn't lament the idea of fragmentation, provisionality, or incoherence, but rather celebrates that.