I've previously written a brief article which discussed how many 'nonsense' koans make perfect sense once you recognize the context of teachings and background information that Japanese Zen students would have had.

The "sound of one hand clapping" koan, for example, is a reference to a teaching to which students would have been exposed prior to the koan in which two methodologies / perspectives interacting were compared to two hands coming together to make a noise.

If viewing things through a binary, dualistic lens produces certain conclusions, what is the conclusion reached when examining the problem in a non-dualistic way instead? That's the question the koan asks.