The holy name of the Lord—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—is a transcendental vibration because it comes from the transcendental platform, the supreme abode of Kṛṣṇa. Because there is no difference between Kṛṣṇa and His name, the holy name of Kṛṣṇa is as pure, perfect and liberated as Kṛṣṇa Himself.
“It is the transcendental nature of the holy names of Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare to transport a man into spiritual madness. Anyone who sincerely chants this holy name very soon attains elevation to the platform of love of God and becomes mad after God. This madness arising from love of God is the first perfectional stage for a human being.”
Excerpted from; Teachings of Lord Caitanya
By His Divine Grace A. C. Bhaktivedanta Swami Prabhupāda
Chapter Eighteen, The Conversations with Prakāśānanda
…In this age of logic, argument and disagreement, the chanting of Hare Kṛṣṇa is the only means for self-realization. Because this transcendental vibration alone can deliver the conditioned soul, it is considered to be the essence of the Vedānta-sūtra. According to the material conception, there is duality between the name, form, quality, emotions and activities of a person and the person himself, but as far as the transcendental vibration is concerned, there is no such limitation, for it descends from the spiritual world. In the spiritual world there is no difference between the name of the person and the quality of the person. Of course in the material world there is a difference. Because the Māyāvādī philosophers cannot understand this, they cannot utter the transcendental vibration.
The Hare Krishna Movement 