A metanarrative is any theory that would attempt to unify and explain all human experience. It is essentially a "worldview" - a deep conviction about the nature of reality that informs the way we view the world, and the way we live our lives. Christianity, atheism, Darwinism, and Marxism are all examples of metanarratives, because each of them attempts to offer a "story" that explains the world and everything in it.
Postmodernists are known for their extreme skepticism toward metanarratives, and any theory claiming universal truth in general. But their skepticism is not simply an unbiased doubt of general theories, it is also the moral position that metanarratives are bad. Postmodernists correctly see how blind dogma has hurt people. And so they reject all dogmas on moral grounds; refusing to consider the possibility that one of them might be true. While it is commendable to want to protect people from harmful ideology, taking a moral position against anything is spurious for the postmodernist, since he is not supposed to believe in objective morals in the first place.
As a consequence of their skepticism toward the universal, postmodernists emphasize the value and importance of knowing "particulars" - specific, individual details of experience - and discriminate against any theory that would attempt to generalize, or make sense of those particulars. So, for example, a postmodernist might want to know the moral practices of an obscure tribe in Africa; but he would find it offensive to ask if the tribe's practices are morally right. Similarly, for many postmodernists it is important to hold strong opinions on music or politics, but passe to have any opinion on the meaning of life. In other words, postmodernists have an intolerance for life's most interesting and (I think) important questions: why are we here? what is good? how can we know? They want the details, but vehemently oppose any attempt to see the "big picture."
Despite all that, I am sympathetic with some postmodern sentiment. I think it is good to know and experience the minutia of life. And I agree that we can often get so caught up in "getting answers" that we miss a lot of important details. It is also true (a four-letter word for postmodernists) that, when we put too much confidence in human reason, we can become arrogant and develop a false certainty that is harmful. The postmodernist is right about all that. However, it does not follow that there is no truth, or that we are incapable of knowing some truth, or that attempting to discover universal truth is somehow bad. That is a silly idea that is impossible to live out, even for the postmodernist. After all, postmodernism itself is a metanarrative.
No one has articulated the absurdity of the postmodern attitude better than G.K. Chesterton. So, I will simply leave you with these brilliant and prescient words that he wrote in his book Heretics, in 1905:
General theories are everywhere condemned; the doctrine of the Rights of Man is dismissed with the doctrine of the Fall of Man. Atheism itself is too theological for us today. Revolution itself is too much of a system; liberty itself is too much of a restraint. We will have no generalizations... We are more and more to discuss details in art, politics, literature. A man's opinion on tram cars matters; his opinion on Botticelli matters; his opinion on all things does not matter. He may turn over and explore a million objects, but he must not find that strange object, the universe; for if he does he will have a religion, and be lost. Everything matters - except everything.