Stopping thought, or quieting the mind, is a term in Zen and other forms of meditation and yoga referring to the achievement of the mental state of samādhi, where the normal mental chatter slows and then stops for brief or longer periods. This may first occur during zazen and other meditation practices.
One author discusses the process of stopping thinking via mindfulness and meditation.[1]
Paradoxically, Zen teaches that the attainment of this state is not through the normal method of intent and application of skill or technique. As stated in the Zen poem Hsin Hsin Ming:
"When you try to stop activity to achieve passivity your very effort fills you with activity. As long as you remain in one extreme or the other you will never know oneness." - Hsin Hsin Ming
In other words, the process becomes a combination of proper technique, acceptance, and returning to or focusing on a familiar state rather than a state achieved through pure force of will.