Mu is a Chinese term often translated as nothing, and has become known through perhaps the most famous Zen koan - Joshu's 'Does a dog have Buddha Nature', more of which another time. What the koan points the student to is something beyond concepts & any intellectualization, to be known directly, our true nature.
What I'd like to speak of here is the way Mu can also be used in other practical ways, as a means for accessing greater focus & clarity & keeping practice fresh and embodied.
In it's truest sense etymologically, no-thing or non-duality are perhaps more helpful than 'nothing' as Mu is not pointing to a void blankness or definitive non-existence.
In The Diamond Sutra, The Buddha affirms: 'Subhuti, wheresoever there are material characteristics there is delusion, but whoso perceives that all characteristics are in fact non-characteristics perceives the Tathagata'. (A name The Buddha referred to himself as, meaning thusness, suchness or as-isness).
You may have noticed that the word Mu is monosyllabic, and phonetically is similar to Aum (Om) when spoken.
Using a short word as a mantra or prayer has been used within all mystical traditions since time immemorial and is found within the Upanishads, Tibetan texts & closer to home within 'The Cloud of Unknowing', the beautiful medieval Christian guide to contemplative prayer, which says: 'And why pierceth it heaven, this little short prayer of one little syllable? Surely because it is prayed with a full spirit, in the height & in the deepness and in the length & the breadth of his spirit that prayeth it'.
To practise this you may want to find somewhere you might not be disturbed & feel self conscious. As with all good practises it can be done in most situations, sitting, standing, walking or lying down, but to begin with sitting in an armchair or better still in Zazen posture would give the ideal conditions to get the hang of it.
Remaining open we abandon conceptualising & deliberate thinking to the wholehearted practise of sounding the word Mu on the out-breath. It's a kind of sigh almost, a relaxed softly mouthed Muuu.
Allow the focus to be on the tanden point, this is approximately two fingers widths under the belly button & within the centre of the body. This may seem simple or difficult, no matter either way just give it your best shot.
On the inbreath we just allow whatever is there, to be there. Whatever arises, arises. The next outbreath - Muuu & so on. After a while you may sense the deep resonance & grounding quality this simple practice brings. Continuing in this way one can become very one-pointed and perhaps blissful even, a lovely side effect!
I recommend experimenting, but as a starting point suggest perhaps half of a period of 25 mins meditation practising in this way, the next 5 mins or so just 'Muuing' inaudibly & internally in conjunction with the breath, with the remainder of the time resting in the ground of your being, without any method at all. Just allowing thoughts and feelings to arise, stay a while and pass of their own accord. No deliberate thinking or trying not to think, simply resting in our own being.
Recently I've found doing this to be extremely profound when allied to simple movements and exercise. Simply exhaling Mu on the outbreath in a way that feels appropriate and experiencing the aliveness of being. It's offered a new and deeply grounding dimension to simple mind/body exercises such as Hachi Danken, Sun Salutations & Makko Ho exercises - the simpler the form the better, excellent for bringing awareness into movement and helping us to embody the non-dual aspect within our lives.
I strongly recommend giving it a whirl.