Once my own teacher explained the role of the koan in Zen training with an easy simile, and I shall quote it here as it ably explains what the koan is: “Needless to say, the task or role of the koan is to help a student open his Zen eye, to deepen his Zen attainment, and to refine his Zen personality. It is a means in Zen training , but in actual practice the koan does not lead a student along an easy and smooth shortcut, like other ordinary means. The koan, on the contrary, throws a student into a steep and rugged maze where he has sense of direction at all. He is expected to overcome all the difficulties and find the way out himself. In other words, the koan is the most difficult and rough means for the student to go through. Good koan, called nanto, are those that are most intricate, illogical, and irrational, in which the most brilliant intellect will completely lose its way.
“Suppose here is a completely blind man who trudges along leaning on his stick and depending on his intuition. The role of the koan is to mercilessly take the stick away from him and to push him down after turning him around. Now the blind man has lost his sole support and intuition and will not know where to go or how to proceed. He will be thrown into he abyss of despair. In this same way, the nanto koan will mercilessly take away all our intellect and knowledge. In short, the role of the koan is not to lead us to satori easily, but on the contrary to make us lose our way and drive us to despair.”
– Zenkei Shibayama, Gateless Barrier: Zen Comments on the Mumonkan