Udaya means awaken. The Kṛṣṇa consciousness is there. In everyone's heart. Simply by śravaṇādi, by pure hearing process... Just like a man is sleeping. The consciousness is there, but he appears to be unconscious. He is sleeping. But if somebody calls him, "Mr. such and such, wake up, wake up. Wake up." So after two, three callings, he wakes up. He remembers, "Oh, I have got to do so many things." Similarly, the Kṛṣṇa consciousness is dormant in everyone's heart.
This Hare Kṛṣṇa mantra is the process of awakening. That's all. This Hare Kṛṣṇa mantra, if we chant repeatedly Hare Kṛṣṇa—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—then the sleeping man awakens to Kṛṣṇa consciousness. This is the process.
Prabhupada's lecture at Christian Monastery - Śrīmad-Bhāgavatam 1.2.5 - Melbourne, April 3, 1972,