A koan is a compact, often baffling story, question or phrase used in the Zen tradition, above all in the Rinzai school, as an object of meditation, given by a teacher to a student to be worked through and "answered" not by reasoning but by a shift in understanding. The best known ask what was one's original face before one's parents were born, or, a later formulation, the sound of one hand clapping. Such questions are designed to be impervious to ordinary thought: they cannot be solved by logic, information or cleverness, and the frustration of the discursive mind's repeated failure to crack them is part of their method. The student is to take the koan up until it fills the whole of attention, sitting with it, carrying it through the day, pressing against it until the conceptual mind exhausts itself and gives way.
The resolution, when it comes, is understood as a direct insight, a kensho or seeing into one's nature, rather than a proposition; and the student demonstrates it to the teacher in the private interview, often without words, the teacher judging from the response whether the seeing is genuine.