"In the first eleven verses of the Caitanya-caritāmṛta, Kṛṣṇadāsa Kavirāja Gosvāmī thus discusses Lord Caitanya Mahāprabhu as Śrī Kṛṣṇa Himself, the Supreme Personality of Godhead, and Lord Nityānanda as Balarāma, the first expansion of Kṛṣṇa. Then in the twelfth and thirteenth verses he describes Advaitācārya, who is another principal associate of Lord Caitanya Mahāprabhu’s and an incarnation of Mahā-Viṣṇu. Thus Advaitācārya is also the Lord, or, more precisely, an expansion of the Lord. The word advaita means 'nondual,' and His name is such because He is nondifferent from the Supreme Lord. He is also called ācārya, teacher, because He disseminated Kṛṣṇa consciousness. In this way He is just like Caitanya Mahāprabhu. Although Lord Caitanya is Śrī Kṛṣṇa Himself, He appeared as a devotee to teach people in general how to love Kṛṣṇa. Similarly, although Advaitācārya is the Lord, He appeared just to distribute the knowledge of Kṛṣṇa consciousness. Thus He is also the Lord incarnated as a devotee."
"Lord Advaita Ācārya is the incarnation of Mahā-Viṣṇu, whose main function is to create the cosmic world through the actions of māyā."
(Caitanya-caritāmṛta Ādi 1.12, Translation)
"Advaita Ācārya is the Lord's partial incarnation, and therefore I offer my obeisances millions of times at His lotus feet."
(Caitanya-caritāmṛta Ādi 1.39, Translation)
"Advaita Ācārya Gosvāmī is an incarnation of the Lord as a devotee. His loud calling was the cause for Kṛṣṇa's incarnation."
(Caitanya-caritāmṛta Ādi 3.92, Translation)
"Mahā-Viṣṇu performs all the functions for the creation of the universes. Śrī Advaita Ācārya is His direct incarnation."
(Caitanya-caritāmṛta Ādi 6.7, Translation)
"Śrī Advaita Ācārya is Lord Caitanya's incarnation as a devotee. Therefore these three tattvas (Caitanya Mahāprabhu, Nityānanda Prabhu and Advaita Gosāñi) are the predominators, or masters."
(Caitanya-caritāmṛta Ādi 7.13, Translation)
"Śrīla Advaita Ācārya Prabhu appeared as an incarnation of a devotee. He is in the category of Kṛṣṇa, but He descended to this earth to propagate devotional service."
(Caitanya-caritāmṛta Ādi 17.298, Translation)
"All glories to Advaita Prabhu, the incarnation of the Supreme Personality of Godhead! He induced Kṛṣṇa to descend and thus delivered the entire world."
(Caitanya-caritāmṛta Antya 8.4, Translation)
"Śrī Caitanya Mahāprabhu, Advaita Prabhu and Nityānanda Prabhu all belong to the viṣṇu-tattva category. Because Lord Caitanya is an ocean of mercy, He is addressed as mahāprabhu, whereas Nityānanda and Advaita, being two great personalities who assist Lord Caitanya, are addressed as prabhu. Thus there are two prabhus and one mahāprabhu. Gadādhara Gosvāmī is a representative of a perfect brāhmaṇa spiritual master. Śrīvāsa Ṭhākura represents a perfect brāhmaṇa devotee. These five are known as the Pañca-tattva."
(Caitanya-caritāmṛta Ādi 17.301, Purport)
Prabhupada: So there are three principles—the īśvara principle and the māyā principle and the jīva principle—these three principles. So Advaita Ācārya is īśvara principle. He belongs to the īśvara group. Even in communistic country, they call "classless society," but they are also creating a managerial class. They cannot do without that. They could not avoid it, managers. Why manager? Make classless society, all worker. That is not possible. There must be īśvara. Īśvara means controller. That is the beginning, from the creation, īśvara.
So īśvara, there are innumerable īśvara forms, as it is stated in the Brahma-saṁhitā. Advaitam acyutam anādim ananta-rūpam (Bs. 5.33). Many, many, many millions and trillions of īśvara form. It is stated in the Bhāgavatam that many... How many, how you can calculate? That is compared—just like in the river or in the ocean there are waves, but you cannot count how many waves are there. That is not possible. Can you count the waves of the ocean, going on, day and night, waves? Similarly, in big, big rivers... So God's incarnation, they are coming out, innumerable, just like the waves, but we can understand by the action that He is incarnation of God.
So the activities of Advaita Ācārya means that He's īśvara. He called Caitanya Mahāprabhu to come down. That is īśvara. You cannot call the Supreme Personality of Godhead to come down. That is not possible. But īśvara, or one who has attained the power of attorney from īśvara, he can do that. It is no otherwise possible. Otherwise, it is impossible. Kṛṣṇa-śakti vinā nahe nāma pracāra. We have to receive the authority from Kṛṣṇa. Then it is possible to preach the cult of Hare Kṛṣṇa movement. That means īśvara, and anyone who attains the power of attorney from īśvara, he's also īśvara. That is called power of attorney. He can act on behalf of the proprietor. That is possible.
So Advaita, Advaita Ācārya, did it. He inaugurated this Kṛṣṇa consciousness movement. When He saw that the people are so much misled that simply they are busy for the bodily necessities of life and completely have forgotten Kṛṣṇa, He became sympathetic. That is Vaiṣṇava behavior. Vaiṣṇavas, they are the best friend of the society, best friend, Vaiṣṇava. Patitānāṁ pāvanebhyo vaiṣṇavebhyo namo namaḥ. The Vaiṣṇava is always thinking how to deliver these fallen souls who are so much captivated with this false philosophy of hedonism—"Eat, drink, be merry and enjoy." This is called hedonism. So they are always thinking how to deliver them. Advaita Prabhu did it; therefore He is īśvara. Prahlāda Mahārāja did it. Any Vaiṣṇava who is actually feeling for the poor conditioned souls, he must make arrangement for delivering these rascals from the death knell of ignorance."
(Srila Prabhupada Lecture, Mayapur, April 5, 1975)
Prabhupada: Sometimes Advaita Ācārya is called Sadāśiva avatāra. The Sadāśiva is also expansion of Mahā-Viṣṇu. So either way you say, incarnation of Sadāśiva or Mahā-Viṣṇu, it doesn't matter. But Advaita Ācārya is īśvara-tattva. He's not śakti-tattva. He's īśvara-tattva. And we are all śakti-tattva. Therefore there is difference. Śakti-śaktimān. Although there is no difference abhinna, but still, śakti-tattva is superior, er, śaktimān tattva is superior than śakti-tattva.
So in this way try to understand Śrī Caitanya Mahāprabhu, Nityānanda Prabhu, Advaita Prabhu, and Gadādhara and śrīvāsādi-gaura-bhakta-vṛnda. And... But they are so kind because they have come to deliver the fallen souls. If you sincerely chant their name, śrī-kṛṣṇa-caitanya prabhu-nityānanda...
Devotees: ...śrī-advaita gadādhara śrīvāsādi-gaura-bhakta-vṛnda.
Prabhupāda: ...they'll be very, very kind to reveal themselves to you, and your path for liberation will be open.
(Srila Prabhupada Lecture, Mayapur, April 5, 1975)