Mu is a Japanese word (wu in Chinese) meaning "no", "not" or "without". In Zen it is known above all from the first case of The Gateless Gate. A monk asks the teacher Zhaozhou whether a dog has Buddha nature, and Zhaozhou answers, "Mu."
Because Buddhist teaching holds that all beings have Buddha nature, the answer cannot simply mean "no". It is usually understood as refusing the terms of the question, pointing past both yes and no.
Mu is often the first koan given to a student. They are asked to keep the single syllable with them, breath after breath, until it stops being a word to think about.