Derrida is the most difficult and most caricatured figure of late twentieth-century philosophy, and the one whose reputation has suffered most from summary.
Deconstruction is not the claim that texts mean whatever a reader wants, which is the version that reached the culture wars. It is a technique of reading that locates the oppositions a text depends on — speech and writing, presence and absence, nature and culture, man and woman — and shows that the privileged term secretly requires the one it subordinates, so that the hierarchy cannot be held. His term différance names the double movement he thought this revealed: meaning both differs (a sign means by not being other signs) and defers (its settlement never arrives), so there is no point at which interpretation touches bottom.
The political charge is indirect but real. If the founding oppositions of Western thought are unstable, then so are the hierarchies built on them, and a great deal of feminist, postcolonial and legal theory took deconstruction as a tool for exactly that. Derrida himself resisted the reduction of his work to a politics and then, late, wrote directly on it — Specters of Marx (1993) defending a "spirit" of Marxism after the collapse of the states that claimed it, and work on hospitality, forgiveness and the death penalty that is closer to conventional ethics than his reputation suggests.
His 1966 lecture at Johns Hopkins is conventionally the moment French theory arrived in America, and the reception there — inside literature departments rather than philosophy — shaped both his influence and the hostility to it. Analytic philosophers largely dismissed him; the 1992 Cambridge honorary degree was contested in public by philosophers who thought the work not serious.