Often, when we approach God in prayer, we do so with a specific agenda or request. The Bhagavad-gita (7.16) explains that four kinds of pious men begin to render devotional service unto the Lord—the distressed, the desirer of wealth, the inquisitive, and he who is searching for knowledge of the Absolute. While praying for relief or material maintenance is certainly pious and better than not approaching God at all, the pure chanting of the Hare Krishna mahāmantra operates on a much higher, unmotivated platform.
Srila Prabhupada explains that the chanting of the Hare Krishna mahāmantra is not a request for our daily bread, nor is it a plea for material facility. The word Hare refers to the internal spiritual energy of the Lord (Srimati Radharani), and Krishna and Rama refer to the Supreme Personality of Godhead Himself, the reservoir of all pleasure. Therefore, the mahāmantra is a sublime petition: "O Supreme Energy of the Lord, O Supreme Lord, please engage me in Your loving service."
This is the essence of pure devotional service (bhakti). Lord Caitanya Mahaprabhu perfectly exemplifies this mood in His Sikshashtakam (Verse 4): na dhanaṁ na janaṁ na sundarīṁ kavitāṁ vā jagad-īśa kāmaye "O almighty Lord, I have no desire to accumulate wealth, nor do I desire beautiful women, nor do I want any number of followers. I only want Your causeless devotional service birth after birth."
Thus, while ordinary prayer may be tied to the temporary conditions of this material world, chanting the holy name is the pure, eternal cry of the soul fully dependent on the Supreme Lord, seeking to simply serve Him with love.