To understand the potency of the Hare Krishna mahāmantra, one must understand the Absolute nature of the Supreme Lord. In the material world, a name and the object it represents are completely different. If you are dying of thirst and simply chant "water, water, water," your thirst will not be quenched. You need the actual substance.
However, in the spiritual realm, there is no difference between the name, the form, the qualities, and the pastimes of the Supreme Lord. The Padma Purana states: nāma cintāmaṇiḥ kṛṣṇas caitanya-rasa-vigrahaḥ / pūrṇaḥ śuddho nitya-mukto ’bhinnatvān nāma-nāminoḥ "The holy name of Krishna is transcendentally blissful. It bestows all spiritual benedictions, for it is Krishna Himself, the reservoir of all pleasure. Krishna's name is complete, and it is the form of all transcendental mellows. It is not a material name under any condition, and it is no less powerful than Krishna Himself. Since Krishna's name is not contaminated by the material qualities, there is no question of its being involved with māyā. Krishna's name is always liberated and spiritual; it is never conditioned by the laws of material nature."
Because Krishna and His name are non-different (abhinnatvān nāma-nāminoḥ), when you chant the Hare Krishna mahāmantra, you are associating directly with the Supreme Personality of Godhead. Just as placing one's hand in a fire will cause the hand to become warm, associating with the supremely pure Lord through His holy name naturally purifies the chanter. The holy name contains all of Krishna's energies, and through sincere chanting, one can realize His divine form, qualities, and eternal pastimes directly.