As a verb, critique means to review or examine something critically. As a noun, a critique is that review or examination, like an art essay or a book report.
The French version of this word is spelled the same (meaning "the art of criticism") and came from the Greek kritike tekhne ("the critical art"). This shouldn't come as a great surprise, since it was the Greeks who gave us such masters of the critique as Socrates, Plato, and Aristotle. Today, through book reports, argument papers, and critical essays, we carry on the tradition of the critique, which is one of the most important skills we'll ever learn in school.