A Zen koan can refer to stories, parables, small statements or even a few words of a phrase that reference a larger story used in the practice of Zen Buddhism. They may be taken from the sayings or accounts of Buddhist teachers from the past or they may originate from modern day. Koans can be studied from a historical or literature perspective or contemplating them can form part of meditative practice.
Meditating on a Zen koan is meant to help the person transcend daily thought patterns to arrive at a more enlightened mental place. Koans can pose questions or puzzles that tend to resist being “solved” by rational thought. Rather, they need to be experienced and pondered to create greater spiritual awareness. There are huge numbers of examples of koans, including the famous, “What is the sound of one hand clapping," which is sometimes just stated as, “What is the sound of one hand.”
From a rational or intellectual perspective, it’s not easy to make sense of such a puzzle. Some people would say a single hand not clapping against another could hardly make a sound. But practitioners of Zen would say trying to answer this question from an intellectual perspective would completely miss the point of this Zen koan. The question is to be experienced and dwelt on in a much more open, meditative manner that bypasses intellectual or realistic thought. Once you are able to not look at this as merely a question to be answered in a rational way, you may come close to finding your own answer.
In the practice of some forms of Buddhism, students or practitioners may be asked to provide answers to a Zen koan after some contemplation. When these answers represent a valid departure from intellectual, there may be no “correct” answer, but rather a number of answers that are equally true. Sometimes students ponder not only a Zen koan question, but also answers from students and spiritual leaders of the past.
There are a number of collections of Zen koan literature, including the revered The Gateless Gate, which was written in the 12th or 13th century CE. Yet you can look outside of Buddhism to discover koans. Many look at the teachings of people like Jesus Christ as full of koans. Like the practice of Zen, some in Christianity believe that you can’t simply “interpret” Christ’s words from an intellectual perspective. You have to go deeper and ponder some of his statements (often in prayer) in order to arrive at a spiritual understanding of what they mean, and many accept that there is no single valid interpretation of things like Christ’s parables.