Caitanya Mahāprabhu informs us that in every country and in every scripture there is some hint of love of Godhead. But no one knows what love of Godhead actually is. The Vedic scriptures, however, are different in that they can direct the individual in the proper way to love God. Other scriptures do not give information on how one can love God, nor do they actually define or describe what or who the Godhead actually is. Although they officially promote love of Godhead, they have no idea how to execute it. But Caitanya Mahāprabhu gives a practical demonstration of how to love God in a conjugal relationship. Taking the part of Śrīmatī Rādhārāṇī, Caitanya Mahāprabhu tried to love Kṛṣṇa as Rādhārāṇī loved Him. Kṛṣṇa was always amazed by Rādhārāṇī’s love. "How does Rādhārāṇī give Me such pleasure?" He would ask. In order to study Rādhārāṇī, Kṛṣṇa lived in Her role and tried to understand Himself. This is the secret of Lord Caitanya's incarnation. Caitanya Mahāprabhu is Kṛṣṇa, but He has taken the mood and role of Rādhārāṇī to show us how to love Kṛṣṇa. Thus the author writes in the fifth verse, “I offer my respectful obeisances unto the Supreme Lord, who is absorbed in Rādhārāṇī’s thoughts.”
This brings up the question of who Śrīmatī Rādhārāṇī is and what Rādhā-Kṛṣṇa is. Actually Rādhā-Kṛṣṇa is the exchange of love—but not ordinary love. Kṛṣṇa has immense potencies, of which three are principal: the internal, the external and the marginal potencies.
(Sri Caitanya Caritamrta--introduction).

To learn how Kṛṣṇa enjoys pleasure, we must study the first nine cantos of Śrīmad-Bhāgavatam, and then we should study the Tenth Canto, in which Kṛṣṇa's pleasure potency is displayed in His pastimes with Rādhārāṇī and the damsels of Vraja. Unfortunately, unintelligent people turn at once to the sports of Kṛṣṇa in the Daśama-skandha, the Tenth Canto. Kṛṣṇa's embracingRādhārāṇī or His dancing with the cowherd girls in the rāsa dance are generally not understood by ordinary men, because they consider these pastimes in the light of mundane lust. They foolishly think that Kṛṣṇa is like themselves and that He embraces the gopīs just as an ordinary man embraces a young girl. Some people thus become interested in Kṛṣṇa because they think that His religion allows indulgence in sex. This is not kṛṣṇa-bhakti, love of Kṛṣṇa, but prākṛta-sahajiyā—materialistic lust.
To avoid such errors, we should understand what Rādhā-Kṛṣṇa actually is. Rādhā and Kṛṣṇa display Their pastimes through Kṛṣṇa's internal energy. The pleasure potency of Kṛṣṇa's internal energy is a most difficult subject matter, and unless one understands what Kṛṣṇa is, one cannot understand it. Kṛṣṇa does not take any pleasure in this material world, but He has a pleasure potency. Because we are part and parcel of Kṛṣṇa, the pleasure potency is within us also, but we are trying to exhibit that pleasure potency in matter. Kṛṣṇa, however, does not make such a vain attempt. The object of Kṛṣṇa's pleasure potency is Rādhārāṇī; Kṛṣṇa exhibits His potency as Rādhārāṇī and then engages in loving affairs with Her. In other words, Kṛṣṇa does not take pleasure in this external energy but exhibits His internal energy, His pleasure potency, as Rādhārāṇī and then enjoys with Her. Thus Kṛṣṇa manifests Himself as Rādhārāṇī in order to enjoy His internal pleasure potency. Of the many extensions, expansions and incarnations of the Lord, this pleasure potency is the foremost and chief.
(Sri Caitanya Caritamrta--introduction).

It is not that Rādhārāṇī is separate from Kṛṣṇa. Rādhārāṇī is also Kṛṣṇa, for there is no difference between the energy and the energetic. Without energy, there is no meaning to the energetic, and without the energetic, there is no energy. Similarly, without Rādhā there is no meaning to Kṛṣṇa, and without Kṛṣṇa there is no meaning to Rādhā. Because of this, the Vaiṣṇava philosophy first of all pays obeisances to and worships the internal pleasure potency of the Supreme Lord. Thus the Lord and His potency are always referred to as Rādhā-Kṛṣṇa. Similarly, those who worship Nārāyaṇa first of all utter the name of Lakṣmī, as Lakṣmī-Nārāyaṇa. Similarly, those who worship Lord Rāma first of all utter the name of Sītā. In any case—Sītā-Rāma, Rādhā-Kṛṣṇa, Lakṣmī-Nārāyaṇa—the potency always comes first.
(Sri Caitanya Caritamrta--introduction).

Rādhā and Kṛṣṇa are one, and when Kṛṣṇa desires to enjoy pleasure, He manifests Himself as Rādhārāṇī. The spiritual exchange of love between Rādhā and Kṛṣṇa is the actual display of Kṛṣṇa's internal pleasure potency. Although we speak of "when" Kṛṣṇa desires, just when He did desire we cannot say. We only speak in this way because in conditioned life we take it that everything has a beginning; however, in spiritual life everything is absolute, and so there is neither beginning nor end. Yet in order to understand that Rādhā and Kṛṣṇa are one and that They also become divided, the question "When?" automatically comes to mind. When Kṛṣṇa desired to enjoy His pleasure potency, He manifested Himself in the separate form of Rādhārāṇī, and when He wanted to understand Himself through the agency of Rādhā, He united with Rādhārāṇī, and that unification is called Lord Caitanya. This is all explained by Śrīla Kṛṣṇadāsa Kavirāja in the fifth verse of the Caitanya-caritāmṛta.
In the next verse the author further explains why Kṛṣṇa assumed the form of Caitanya Mahāprabhu. Kṛṣṇa desired to know the glory of Rādhā’s love. "Why is She so much in love with Me?" Kṛṣṇa asked. "What is My special qualification that attracts Her so? And what is the actual way in which She loves Me?" It seems strange that Kṛṣṇa, as the Supreme, should be attracted by anyone's love. A man searches after the love of a woman because he is imperfect—he lacks something. The love of a woman, that potency and pleasure, is absent in man, and therefore a man wants a woman. But this is not the case with Kṛṣṇa, who is full in Himself. Thus Kṛṣṇa expressed surprise: "Why am I attracted by Rādhārāṇī? And when Rādhārāṇī feels My love, what is She actually feeling?" To taste the essence of that loving exchange, Kṛṣṇa made His appearance in the same way that the moon appears on the horizon of the sea. Just as the moon was produced by the churning of the sea, by the churning of spiritual loving affairs the moon of Caitanya Mahāprabhu appeared. Indeed, Lord Caitanya's complexion was golden, just like the luster of the moon. Although this is figurative language, it conveys the meaning behind the appearance of Caitanya Mahāprabhu.
(Sri Caitanya Caritamrta--introduction).

Vṛndāvana is actually experienced as it is by persons who have stopped trying to derive pleasure from material enjoyment. "When will my mind become cleansed of all hankering for material enjoyment so I will be able to see Vṛndāvana?" one great devotee asks. The more Kṛṣṇa conscious we become and the more we advance, the more everything is revealed as spiritual. Thus Kṛṣṇadāsa Kavirāja Gosvāmī considered the Vṛndāvana in India to be as good as the Vṛndāvana in the spiritual sky, and in the sixteenth verse of the Caitanya-caritāmṛta he describes Rādhārāṇī and Kṛṣṇa as seated beneath a wish-fulfilling tree in Vṛndāvana, on a throne decorated with valuable jewels. There Kṛṣṇa's dear gopī friends serveRādhā and Kṛṣṇa by singing, dancing, offering betel nuts and refreshments, and decorating Their Lordships with flowers. Even today in India people decorate swinging thrones and re-create this scene during the month of July–August. Generally at that time people go to Vṛndāvana to offer their respects to the Deities there.
(Sri Caitanya Caritamrta--introduction).

The author of Śrī Caitanya-caritāmṛta offers his respectful obeisances unto the three Deities of Vṛndāvana named Śrī Rādhā-Madana-mohana, Śrī Rādhā-Govindadeva and Śrī Rādhā-Gopīnāthajī. These three Deities are the life and soul of the Bengali Vaiṣṇavas, or Gauḍīya Vaiṣṇavas, who have a natural aptitude for residing in Vṛndāvana. The Gauḍīya Vaiṣṇavas who follow strictly in the line of Śrī Caitanya Mahāprabhu worship the Divinity by chanting transcendental sounds meant to develop a sense of one's transcendental relationship with the Supreme Lord, a reciprocation of mellows (rasas) of mutual affection, and, ultimately, the achievement of the desired success in loving service. These three Deities are worshiped in three different stages of one's development. The followers of Śrī Caitanya Mahāprabhu scrupulously follow these principles of approach.
(Sri Caitanya Caritamrta--1:1:19----purport).

Lord Śrī Caitanya Mahāprabhu explained this mode of devotional service in three stages, and therefore these worshipable Deities were installed in Vṛndāvana by different Gosvāmīs. They are very dear to the Gauḍīya Vaiṣṇavas there, who visit the temples at least once a day. Besides the temples of these three Deities, many other temples have been established in Vṛndāvana, such as the temple of Rādhā-Dāmodara of Jīva Gosvāmī, the temple of Śyāmasundara of Śyāmānanda Gosvāmī, the temple of Gokulānanda of Lokanātha Gosvāmī, and the temple of Rādhā-ramaṇa of Gopāla Bhaṭṭa Gosvāmī. There are seven principal temples over four hundred years old that are the most important of the five thousand temples now existing in Vṛndāvana.
(Sri Caitanya Caritamrta--1:1:19----purport).

Because of his development of transcendental attachment for the Supreme Lord, a surrendered soul feels the presence of his beloved everywhere, and all his senses are engaged in the loving service of the Lord. His eyes are engaged in seeing the beautiful couple Śrī Rādhā and Kṛṣṇa sitting on a decorated throne beneath a desire tree in the transcendental land of Vṛndāvana. His nose is engaged in smelling the spiritual aroma of the lotus feet of the Lord. Similarly, his ears are engaged in hearing messages from Vaikuṇṭha, and his hands embrace the lotus feet of the Lord and His associates. Thus the Lord is manifested to a pure devotee from within and without. This is one of the mysteries of the devotional relationship in which a devotee and the Lord are bound by a tie of spontaneous love. To achieve this love should be the goal of life for every living being.
(Sri Caitanya Caritamrta--1:1:55----purport).

Cintāmaṇi was a prostitute with whom Bilvamaṅgala was intimate earlier in his life. She gave him the inspiration to begin on the path of devotional service, and because she convinced him to give up material existence to try for perfection by loving Kṛṣṇa, he has first offered his respects to her. Next he offers his respects to his initiating spiritual master, Somagiri, and then to the Supreme Personality of Godhead, who was also his instructing spiritual master. He explicitly mentions Bhagavān, who has peacock feathers on His crown, because the Lord of Vṛndāvana, Kṛṣṇa the cowherd boy, used to come to Bilvamaṅgala to talk with him and supply him with milk. In his adoration of Śrī Kṛṣṇa, the Personality of Godhead, he states that Jayaśrī, the goddess of fortune, Śrīmatī Rādhārāṇī, takes shelter in the shade of His lotus feet to enjoy the transcendental rasa of nuptial love. The complete treatise Kṛṣṇa-karṇāmṛta is dedicated to the transcendental pastimes of Śrī Kṛṣṇa and Śrīmatī Rādhārāṇī. It is a book to be read and understood by the most elevated devotees of Śrī Kṛṣṇa.
(Sri Caitanya Caritamrta--1:1:57----purport).

(8) From the Ananta-saṁhitā:
ya eva bhagavān kṛṣṇo
rādhikā-prāṇa-vallabhaḥ
sṛṣṭy ādau sa jagan-nātho
gaura āsīn maheśvari
"The Supreme Person, Śrī Kṛṣṇa Himself, who is the life of Śrī Rādhārāṇī and is the Lord of the universe in creation, maintenance and annihilation, appears as Gaura, O Maheśvarī."
(Sri Caitanya Caritamrta--1:2:22----purport).