A koan is a brief story, dialogue or question from the Zen tradition, given to a student as a focus for practice. The best known is "What is the sound of one hand?"
Koans are not riddles with clever answers. They are designed to be unsolvable by ordinary reasoning, so that the student has to stay with the question itself. In traditional training this is done with a teacher over months or years.
The word is the Japanese reading of the Chinese gong'an, "public case", in the sense of a legal precedent. The major collections were compiled in China between the eleventh and thirteenth centuries.