WordNet (r) 3.0 (2006):

koan
    n 1: a paradoxical anecdote or a riddle that has no solution;
         used in Zen Buddhism to show the inadequacy of logical
         reasoning

The Jargon File (version 4.4.7, 29 Dec 2003):

koan
 /koh'an/, n.

    A Zen teaching riddle. Classically, koans are attractive paradoxes to be
    meditated on; their purpose is to help one to enlightenment by temporarily
    jamming normal cognitive processing so that something more interesting can
    happen (this practice is associated with Rinzai Zen Buddhism). Defined here
    because hackers are very fond of the koan form and compose their own koans
    for humorous and/or enlightening effect. See Some AI Koans, has the X
    nature, hacker humor.