What is the meaning and importance of Japa?  What is its value and how should one do it?

 “The japa is usually successful only on one of two conditions—if it is repeated with a sense of its significance, a dwelling of something in the mind on the nature, power, beauty, attraction of the Godhead it signifies and is to bring into the consciousness,— that is the mental way; or if it comes up from the heart or rings in it with a certain sense or feeling of bhakti making it alive,— that is the emotional way. Either the mind or the vital has to give it support or sustenance. But if it makes the mind dry and the vital restless, it must be missing that support and sustenance. There is, of course, a third way, the reliance on the power of the mantra or name in itself; but then one has to go on till that power has sufficiently impressed its vibration on the inner being to make it at a given moment suddenly open to the Presence or the Touch. But if there is a struggling or insistence for the result, then this effect which needs a quiet receptivity in the mind is impeded. That is why I insisted so much on mental quietude and not on too much straining or effort, to give time to allow the psychic and the mind to develop the necessary condition of receptivity—a receptivity as natural as when one receives an inspiration for poetry and music. It is also why I do not want you to discontinue your poetry—it helps and does not hinder the preparation, because it is a means of developing the right position of receptivity and bringing out the bhakti which is there in the inner being. To spend all the energy in japa or meditation is a strain which even those who are accustomed to successful meditation find it difficult to maintain—unless in periods when there is an uninterrupted flow of experiences from above.
[SABCL, 23:745]

OM: The Supreme Mantra

OM is the signature of the Lord.
[CWM2, 15:33]
 OM is the mantra, the expressive sound-symbol of the Brahman Consciousness in its four domains from the Turiya to the external or material plane. The function of a mantra is to create vibrations in the inner consciousness that will prepare it for the realisation of what the mantra symbolises and is supposed indeed to carry within itself. The mantra OM should therefore lead towards the opening of the consciousness to the sight and feeling of the One Consciousness in all material things, in the inner being and in the supraphysical worlds, in the causal plane above now superconscient to us and, finally, the supreme liberated transcendence above all cosmic existence. The last is usually the main preoccupation with those who use the mantra.
[SABCL, 23:745-46]
In this yoga there is no fixed mantra, no stress is laid on mantras, although sadhaks can use one if they find it helpful or so long as they find it helpful. The stress is rather on an aspiration in the consciousness and a concentration of the mind, heart, will, all the being. If a mantra is found helpful for that, one uses it. OM if rightly used (not mechanically) might very well help the opening upwards and outwards (cosmic consciousness) as well as the descent.”
[SABCL, 23:746]

Mantra Yoga

As when the mantra sinks in Yoga’s ear,
Its message enters stirring the blind brain
And keeps in the dim ignorant cells its sound;
The hearer understands a form of words
And, musing on the index thought it holds,
He strives to read it with the labouring mind,
But finds bright hints, not the embodied truth:
Then, falling silent in himself to know
He meets the deeper listening of his soul:
The Word repeats itself in rhythmic strains:
Thought, vision, feeling, sense, the body’s self
Are seized unutterably and he endures
An ecstasy and an immortal change;
He feels a Wideness and becomes a Power,
All knowledge rushes on him like a sea:
Transmuted by the white spiritual ray
He walks in naked heavens of joy and calm,
Sees the God-face and hears transcendent speech:
[CWSA, 33-34:375]