The best three word summary I've heard of postmodernism comes to us from Jean-François Lyotard: "Incredulity toward metanarratives." This is about as throrough as a three word summary can get, though it often leads to more questions. It relates to sirwfc718's assessment of relativism, but also offers something of a view as to why one arrives at that vantage point.

The term was originally an architectural term, and described specific reactions against the modernist ideals of design, and would, if memory serves, usually involve some sort of inversion or confounding of modernism's bold, powerful, often simple and unequivocal lines and patterns. I forget who it was who said it, but someone brilliant said that the quintessential postmodern experience was to merely observe the modern (by which I mean contemporary here) cityscape, which features buildings from all eras standing side by side, in a perpetual state of disjunction. It's basically a collage which conforms to no overarching style or social rubric, and therefore offers no unified message, (except for the message of disunity).

It then became applied post-hoc to a wide variety of movements in other media, and in thought itself, but it has never been a movement in any monolithic sense (indeed, the essence of the thing defies the creation of anything monolithic) which is what makes it so difficuly -- or impossible, really, I would say -- to provide an adequate, all encompassing definition or category. All of the works I've seen mentioned here across the arts seem related to the non-movement.

The term only came into existence in the 20th century, which sort of prohibits the admission of fine fellows like Matthew Arnold. However, Dover Beach (love that poem, by the way, thanks for mentioning it, ecib) clearly demonstrates that the postmodern shift was prefigured in previous ones, especially those that occurred at the cusp where British romanticism bleeds into the Victorian era. This type of grand and tragic wrestling with doubt and loss of meaning is quite common in that time, where all over society, writers are struggling to hold onto the view of the world they've accepted all their lives, attempting to reconcile it with the discoveries and theories of the time (Darwin's work plays a major role in this upset). Tennyson's "In Memoriam" is another epic chronicle of such struggle with doubt. The parallel's to postmodernism as described by Lyotard are clear: the introduction of doubt into a particular metanarrative.

The issue is further clouded by being confused with poststructuralism, a movement which takes place in philosophy and semiotics. The ideas of this movement stirs the kettle of all this postmodern foment, but the two are in no means one and the same. Reading Derrida is fun if you like your cerebellum to twist in knots. It's probably better to read about him at first, and the stanford encyclopedia of philosophy is a good place to start. (If you really want to subject yourself to all that).