Koan in Zen Buddhism is a problem or riddle that admits no logical solution. (Korean: 공안, Chinese: 公案) The term is a compound word, consisting of the characters 公 “public; official; governmental; common; collective; ” and 案 “table; desk; (law) case; record.”
A kōan is a story, dialogue, question, or statement. The continuous pondering of the koan leads to an initial insight into the Buddha-nature.
See the Kwan Um School of Zen for more information about kong-an practice. I received my first koan interview and heard a few koan readings, but koans are mysterious to me.
선문답 Zen riddle, koan