Read more about PsychicBeing from the works of the Mother and Sri Aurobindo.
What is the Psychic Being?
It is the soul in evolution.
The psychic being is a divine nucleus in each human being which stands behind mind, life and body but of which we are only dimly aware. It is a portion of the Divine that persists after death and permanent from life to life, taking the experience of life through its outer instruments. As this experience grows it manifests a developing psychic personality which insisting always on the good, true and beautiful, finally becomes ready and strong enough to turn the nature towards the Divine.  
The psychic being is formed progressively around this divine centre, the soul, in the course of its innumerable lives in the terrestrial evolution, until the time comes when the psychic being, fully formed and wholly awakened, becomes the conscious sheath of the soul around which it is formed. And thus identified with the Divine, it becomes His perfect instrument in the world.  The psychic being is that which persists after death, because it is your eternal self; it is this that carries the consciousness forward from life to life. 
The psychic being is in the heart centre in the middle of the chest (not in the physical heart, for all the centres are in the middle of the body), but it is deep behind. 
Why is the Psychic Being Important?
Establishing contact with the psychic being can help when one feels a difficulty or there is a problem to be solved, when one wants to make progress, overcome obstacles or conquer depression. It also brings the joy of identification, for it is an experience that gives a very concrete joy. 
Role of the Psychic Being
When the psychic is active, it can give a clear intimation of what is true and false, divine or not, right or wrong and repel all invasion of hostile forces. 
The contribution of the psychic being to the sadhana is: (1) love and bhakti, a love not vital, demanding and egoistic but without conditions or claims, self-existent; (2) the contact or the presence of the Mother within; (3) an unerring guidance from within; (4) a quieting and purification of the mind, vital and physical consciousness by their subjection to the psychic influence and guidance; (5) the opening up of the lower consciousness to the higher spiritual consciousness above for its descent into one who is prepared to receive it with a complete receptivity—for the psychic brings right thought, right perception, right feeling and right attitude. 
For Transforming Parts of the Being
If the psychic is awake and in front, it becomes easy to remain conscious of the things that have to be changed in the external nature and it is comparatively easy too to change them. But if the psychic gets veiled and retires into the background, the outer nature left to itself finds it difficult to remain conscious of its own wrong movements and even with great effort cannot succeed in getting rid of them…. the psychic active and awake the right attitude comes naturally and whatever difficulty there was soon diminishes or even disappears.
If the psychic and mental parts in us are strong, the vital comes under mastery and direction to an extent hardly possible to the surface mentality; even the body and the physical energies can be taken up by the inner mind and will and turned into a more plastic instrumentation of the soul, the psychic being. 
How to Connect to the Psychic Being?
The mind (thoughts and beliefs) and vital (emotions and desires) must be quietened, purified and transformed. 
One has to aspire for discrimination in the mind, purity in the vital, calm equanimity, enduring patience, absence of pride and especially the development of the psychic being through surrender, self-giving, psychic humility and devotion. 
Concentration and Meditation
One can concentrate in any of the three centres below, which is easiest to the sadhak or gives most result.
Above the head: to bring peace, silence, liberation from the body sense, the identification with mind and life, facilitate Divine descent and open the way for the lower (mental-vital-physical) consciousness to rise up and meet the higher Consciousness. Between the eyebrows: to liberate the inner mind and vision, to awaken Yogic consciousness Heart centre: opened by aspiration, love, bhakti, surrender 
One can fix a time every day when one can be free and undisturbed; sit comfortably and think of one’s psychic being with an aspiration to enter into contact with it, and not be discouraged if success is not immediate. 
One can detach oneself and look at the activities of the body, mind and vital as if they were not one’s own but a mechanical action of Nature. By being a disinterested witness, one can become aware of an inner being which is separate, calm and uninvolved in Nature. 
Obstacles appear when some part of the being is not fully prepared or open. One has to meet these with a patient and persistent aspiration and a quiet vigilance of self-introspection that will bring about the necessary opening. 
Evolution of the Psychic Being
The spirit is the Self that is not affected by the evolution, it is above it. The psychic is the soul that develops in the evolution, only it is covered or concealed by the activity of mind, vital and body. 
The psychic being at its origin is only a spark of the divine consciousness and it is through successive lives that it builds up a conscious individuality. There comes a time when the being is fully developed, fully individualised, fully master of itself and its destiny. When this being or one of these psychic beings has reached that stage and takes birth in a human being, that makes a very great difference: the human being, so to say, is born free. Psychic being will no longer be bound by the necessity of coming upon earth, it will have completed its development and will be able to choose freely either to consecrate itself to the divine Work or go elsewhere, that is, in the higher worlds.  
Read more about Psychic Being from the works of the Mother and Sri Aurobindo.