Deconstruction is an approach to literary theory created by postmodern philosopher Jacques Derrida. Derrida categorized it as a derivative of Marxism, with which it shares a logical basis (Hegelian dialectic) and methodology (aggressive hunting of deep-set "contradictions").
Its signature argumentative move is to establish a binary opposition—for instance, male and female—and then show how, rather than being clear cut opposites, each concept is in fact very much wrapped up in the other. This is often because each one, rather than being positively defined, is actually defined largely in terms of the other. Once the binary opposition has been shown to be less strict than assumed, it is used to show how a literary text contradicts itself, revealing more ambiguity than many other methods of interpretation.
Deconstruction was enormously controversial in the 1980s, due largely to a combination of its adherents making extremely provocative claims and its critics having trouble understanding the often very difficult writings of Derrida and his followers. These days there are relatively few strict deconstructionists in English departments, and the approach has largely become one of many tools used.
Criticism of deconstruction usually centers on a couple of key aspects. First is the allegedly excessive difficulty of the writings of major deconstructionists. Second is the argument that reducing texts to conflicted ambiguities is nihilistic, or amounts to a claim that communication is impossible. The first is true, although proponents of deconstruction often ask why this is considered a problem with deconstruction when it is not considered a problem in other fields. (One rarely sees the criticism that quantum physics is wrong because it is very hard to understand, for instance.) The second would largely be denied by deconstructionists, and has been vociferously denied at several points by Derrida, who was in fact extremely politically active, and a ferociously savage critic of those who he felt misunderstood his writings.
Having largely peaked as a school of thought in the 1980s, the term has largely become a generic term referring to any work that actively displays and dismantles its components. For example, deconstructionist food refers to things like "salads" that consist of the various ingredients of the salad laid out separately and individually on a plate. Such things have little to nothing to do with anything Derrida has ever said or written.