The meaning of Hare Krishna Chanting from Srila Prabhupada, the Spiritual Master of Entire Hare Krishna movement itself:
This transcendental vibration--by chanting of Hare Krsna, Hare Krsna, Krsna Krsna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare--is the sublime method for reviving our Krsna consciousness. As living spiritual souls we are all originally Krsna conscious entities, but due to our asociation with matter since time immemorial, our consciousness is now poluted by material atmosphere. In this polluted concept of life, we are all trying to exploit the resources of material nature, but actually we are becoming more and more entangled in our complexities. This illusion is called maya, or hard struggle for existence over the stringent laws of material nature. This illusory struggle against the material nature can at once be stopped by revival of our Krsna consciousness.
Krsna consciousness is not an artificial imposition on the mind. This consciousness is the original energy of the living entity. When we hear the transcendental vibration, this consciousness is revived. And the process is recommended by authorities for this age. By practical experience also, we can perceive that by chanting this maha-mantra, or the Great Chanting for Deliverance, one can at once feel transcendental ecstasy from the spiritual stratum. When one is factually on the plane of spiritual understanding, surpassing the stages of sense, mind and intelligence, one is situated on the transcendental plane. This chanting of Hare Krsna, Hare Krsna, Krsna Krsna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare is directly enacted from the spiritual platform, surpassing all lower states of consciousness--namely sensual, mental and intellectual. There is no need of understanding the language of the mantra, nor is there any need of mental speculation nor any intellectual adjustment for chanting this maha-mantra. It springs automatically from the spiritual platform, and as such, anyone can take part in this transcendental sound vibration, without any previous qualification, and dance in ecstasy.
We have seen it practically. Even a child can take part in the chanting, or even a dog can take part in it. The chanting should be hears, however, from the lips of a pure devotee of the Lord, so that immediate effect can be achieved. As far as possible, chanting from the lips of a nondevotee should be avoided, as much as milk touched by the lips of a serpent causes poisonous effect.
The word Hara is a form of addressing the energy of the Lord. Both Krsna and Rama are forms of addressing directly the Lord, and they mena " the highest pleasure, eternal." Hara is the supreme pleasure potency of the Lord. This potency, when addressed are Hare, helps us in reaching the Supreme Lord.
The material energy, called as maya, is also one of the multipotencies of the Lord, as much as we are also marginal potency of the Lord. The living entities are described as superior energy than matter. When the superior energy is in contact with inferior energy, it becomes an incompatible situation. But when the supreme marginal potency is in contact with the spiritual potency, Hara,it becomes the happy, normal condition of the living entity.
The three words, namely Hara, Krsna and Rama, are transcendental seeds of the maha-mantra, and the chanting is a spiritual call for the Lord and His internal energy, Hara, for giving protection to the conditioned soul. The chanting is exactly like a genuine cry by the chold for the mother. Mother Hara helps in achieving the grace of the supreme father, Hari, or Krsna, and the Lord reveals Himself to such a sincere devotee.
No other means, therefore, of spiritual realization is as effective in this age, as chanting the maha-mantra, Hare Krsna, Hare Krsna, Krsna Krsna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare.
http://introduction.krishna.org/Articles/2000/07/00035.html