What is a koan?

it means your fingers slipped when typing
(look at the keyboard and you’ll get it )

A kō-an (公案; Korean: gong’an, Japanese: kōan, Chinese: gōng-à n, Vietnammese: công án) is a story, dialogue, question, or statement in the history and lore of Chán (Zen) Buddhism, generally containing aspects that are inaccessible to rational understanding, yet that may be accessible to intuition. A famous kōan is, “Two hands clap and there is a sound; what is the sound of one hand?” (oral tradition, attributed to Hakuin Ekaku, 1686-1769, considered a reviver of the kōan tradition in Japan).

do you mean koran?

A koan is a zen poem or saying that makes a fat lot of no sense at all.
Check out the Zen question of the day.

A kō-an (公案; Korean: gong’an, Japanese: kōan, Chinese: gōng-à n, Vietnammese: công án) is a story, dialogue, question, or statement in the history and lore of Chán (Zen) Buddhism, generally containing aspects that are inaccessible to rational understanding, yet that may be accessible to intuition. A famous kōan is, “Two hands clap and there is a sound; what is the sound of one hand?” (oral tradition, attributed to Hakuin Ekaku, 1686-1769, considered a reviver of the kōan tradition in Japan).

not a clue

It is that waste of money sculpture outside St Marys Hospital at Newport on the Isle of Wight.
Basically it is a smaller version of that Gherkin thing in London although it predates the London one by a few years.
I hope this answers your question in some way.

http://en.wikipedia.org/wiki/Koan

A Zen Parable

Now that some others have filled you in on what a koan is…here is one of my favorites:
The Turtle in the Garden
A monk saw a turtle in the garden of Daizui’s monastery and asked the teacher, “All beings cover their bones with flesh and skin. Why does this being cover its flesh and skin with bones?” Master Daizui took off one of his sandals and covered the turtle with it.

a paradox that if you follow can take you beyond your rational mind.
The world as a mirror of ourselves, but where does the mirror come from?

The aim of the training in a Zen monastery is to enable the monks to achieve very deep insight into the true nature of existence.
A koan is a ‘nonsense’ question which, although it cannot be solved by the rational mind, does have an answer.
Very early in the morning monks go in to the master’s room and give the best answer they can to the Koan – but it’s always wrong.
The pressure is very intense. They meditate for many hours a day, trying to solve their Koan.
The, one day, in a flash of spiritual insight they actually ‘get’ it!
Now when they enter the master’s room, he smiles. They have solved their Koan.

A koan is a koan.

I really don’t know.