Stillness is a great discipline; it is the great discovery of meditation. Stillness becomes the dynamic of transcendence. The more still we are, the more we transcend our limitations. Now, stillness does not mean stopping. It is not static. We fully experience stillness when we feel how it is part of the whole process of growth in nature. There is a wondrous relationship between stillness and growth.

Laurence Freeman, Tasting Wisdom

Stillness seems to be inseparable from surrender. Stillness is not possible in the midst of inner warfare; though, in the inner life, to surrender does not mean to give in so much as to let go, and in this there is an immense simplicity, a lack of complication, of rules and prescriptions. Cynthia Bourgeault (she is contrasting Centering Prayer with other methods such as vipassana, and meditation using a mantra):

A surrender method is even simpler. One does not even watch or label the thought as it comes up, takes form, and dissipates. As soon as it emerges into consciousness, one simply lets it go. The power of this form of meditation does not reside in a particular clarity of the mind or even in presence, but entirely in the gesture of release itself.

Centering Prayer and Inner Awakening, p.20

Eckhart Tolle has explained this particularly well. One of the great strengths of his approach to the contemplative life must be his gentle but steadfast refusal to adopt the terminology of any religion, without rejecting their inner meaning and resonance. It might be too easy to pass by Tolle due to the popularity of his books a few years ago; that would be a mistake – his work is uniquely valuable, if only to serve as a bridge between Buddhist or Advaita based methods and the Christian practices like Centering Prayer and Christian Meditation (WCCM) which have their roots firmly set in their religious foundations. In his remarkably useful little book, Practicing the Power of Now, Eckhart Tolle writes (p.20),

When a thought subsides, you experience a discontinuity in the mental stream — a gap of “no-mind.” At first, the gaps will be short, a few seconds perhaps, but gradually they will become longer. When these gaps occur, you feel a certain stillness and peace inside you. This is the beginning of your natural state of felt oneness with Being, which is usually obscured by the mind.

With practice, the sense of stillness and peace will deepen. In fact, there is no end to its depth. You will also feel a subtle emanation of joy arising from deep within: the joy of Being.