Sri Krsna and His beautiful consort Srimati Radharani.

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī. 

It is explained by the Gosvāmīs that Rādhārāṇī is the manifestation of the pleasure potency of the Supreme Personality of Godhead.

When the Supreme Lord wants to derive transcendental pleasure, He has to create a woman from His internal potency and that women is Srimati Radharani." (SB Canto 3 Ch 31 text 38, Purport)

Srila Prabhupada - "Kṛṣṇa and Rādhārāṇī are both transcendentally qualified, and both of Them attract one another. Yet in that transcendental attraction, Rādhārāṇī is greater than Kṛṣṇa, for the attractiveness of Rādhārāṇī is the transcendental taste in conjugal love. Similarly, there are transcendental tastes in servitude, friendship and other relationships with Kṛṣṇa. Rādhārāṇī is the only gopī who is dearer to Kṛṣṇa than all the other gopīs." (Teachings of Lord Caitanya, (TLC) Ch 14, Purport)

Caitanya Caritāmṛta - "Rādhā and Kṛṣṇa are "one and the same", but They have assumed two bodies. Thus They enjoy each other, tasting the mellows of love.

The two transcendentalists Rādhā and Kṛṣṇa are a puzzle to materialists. The description of Rādhā and Kṛṣṇa from the diary of Śrīla Svarūpa Dāmodara Gosvāmī is a condensed explanation, but one needs great spiritual insight to understand the mystery of these two personalities.

One is enjoying as two.

Śrī Kṛṣṇa is the potent factor, and Śrīmatī Rādhārāṇī is the internal potency. According to Vedānta philosophy, there is no difference between the potent and the potency; they are identical. We cannot differentiate between one and the other, any more than we can separate fire from heat.

Everything in the Absolute is inconceivable in relative existence. Therefore in relative cognizance it is very difficult to assimilate this truth of the oneness between the potent and the potency.

The philosophy of inconceivable oneness and difference propounded by Lord Caitanya is the only source of understanding for such intricacies of transcendence.

In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa.

Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee.

The very name “Rādhā” suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. As such, She is the medium transmitting the living entities’ service to Śrī Kṛṣṇa. Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa." (CC Adi 4.56, Translation and Purport)

Srila Prabhupada - "As Kṛṣṇa is the highest emblem of spiritual perfection, so Rādhārāṇī is the highest emblem of that spiritual pleasure potency by which Kṛṣṇa is satisfied. Since Kṛṣṇa is unlimited, in order to satisfy Him Rādhārāṇī is also unlimited. Kṛṣṇa is satisfied just by seeing Rādhārāṇī, but Rādhārāṇī expands Herself in such a way that Kṛṣṇa desires to enjoy Her more. Because Kṛṣṇa was unable to estimate the pleasure potency of Rādhārāṇī, He decided to accept the role of Rādhārāṇī, and that combination is Śrī Caitanya Mahāprabhu." (Teachings of Lord Caitanya, (TLC) Ch 31)

Caitanya Caritāmṛta -"Radharani's mind, senses and body are steeped in love for Kṛṣṇa, she is Kṛṣṇa’s own energy, and She helps Him in His pastimes. Śrīmatī Rādhārāṇī is as fully spiritual as Kṛṣṇa, no one should consider Her to be material. She is definitely not like the conditioned souls, who have material bodies, gross and subtle, covered by material senses.

She is all-spiritual, and both Her body and Her mind are of the same spiritual embodiment. Because Her body is spiritual, Her senses are also spiritual. Thus Her body, mind and senses fully shine in love of Kṛṣṇa. She is the personified hlādinī-śakti (the pleasure-giving energy of the Lord’s internal potency), and therefore She is the only source of enjoyment for Śrī Kṛṣṇa.

Śrī Kṛṣṇa cannot enjoy anything that is internally different from Him, therefore Rādhā and Kṛṣṇa are identical. The sandhinī portion of Śrī Kṛṣṇa’s internal potency has manifested the all-attractive form of Śrī Kṛṣṇa, and the same internal potency, in the hlādinī feature, has presented Śrīmatī Rādhārāṇī, who is the attraction for the all-attractive. No one can match Śrīmatī Rādhārāṇī in the transcendental pastimes of Śrī Kṛṣṇa." (CC Adi 4.71, Translation and Purport)

Caitanya Caritāmṛta - "Śrī Rādhā is the full power, and Lord Kṛṣṇa is the possessor of full power. The two are not different, as evidenced by the revealed scriptures. The attitude of Śrīmatī Rādhārāṇī is the highest perfection of conjugal love." (CC Adi 4.96, Translation)

Caitanya Caritāmṛta - "That supreme ecstasy of Śrīmatī Rādhārāṇī is the essence of spiritual life. Her only business is to fulfill all the desires of Kṛṣṇa." (CC Madhya 8.164, Translation)

Caitanya Caritāmṛta - "Śrīmatī Rādhārāṇī is the topmost spiritual gem, and the other gopīs—Lalitā, Viśākhā and so on-are expansions of Her spiritual body." (CC Madhya 8.165, Translation)

Srila Prabhupada - "Lord Caitanya exhibited the mode of Śrīmatī Rādhārāṇī when She was contacted from Dvārakā by Śrī Kṛṣṇa. 

Such transcendental love is not possible for any common man; therefore one should not imitate the highest perfectional stage exhibited by Caitanya Mahāprabhu. 

If, however, one desires to be in that association, he may follow in the footsteps of the gopīs. 

In the Padma Purāṇa it is stated that just as Rādhārāṇī is dear to Kṛṣṇa, similarly the kuṇḍa known as Rādhākuṇḍa is also very dear to Him. Rādhārāṇī is the only gopī who is dearer to Kṛṣṇa than all the other gopīs. 

In Śrīmad Bhāgavatam Canto 10 Ch 30 text 28 it is also stated that Rādhārāṇī and the gopīs render the highest perfectional loving service to the Lord and that the Lord is so pleased with them that He does not wish to leave the company of Śrīmatī Rādhārāṇī."(Teachings of Lord Caitanya, Ch 30)

Caitanya Caritāmṛta - "Of all the gopīs, Śrīmatī Rādhārāṇī is the chief. She is a jewel mine of ecstatic love and the source of all purified transcendental conjugal mellows." (CC Madhya 14.160, Translation)

Caitanya Caritāmṛta - "The transcendental goddess Śrīmatī Rādhārāṇī is the direct counterpart of Lord Śrī Kṛṣṇa, She is the central figure for all the goddesses of fortune. She possesses all the attraction to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord." (CC Madhya 23.68, Translation)

Srila Prabhupada - "The fact is that both Kṛṣṇa and Lord Caitanya are the original Personality of Godhead. No one should try to eliminate Lord Caitanya from Śrī Kṛṣṇa. 

In His form of Śrī Kṛṣṇa, He is the supreme enjoyer, and in His form of Lord Caitanya, He is the supreme enjoyed. 

No one can be more superexcellently attractive than Śrī Kṛṣṇa, and but for Śrī Kṛṣṇa, no one can enjoy the supreme form of devotion, Śrīmatī Rādhārāṇī. But for Śrī Kṛṣṇa, all Viṣṇu forms are lacking this ability. 

This is explained in the description of Govinda in Caitanya-caritāmṛta. There it is said that Śrīmatī Rādhārāṇī is the only personality who can infuse Śrī Kṛṣṇa with transcendental pleasure. 

Thus Śrīmatī Rādhārāṇī is the chief damsel of Vraja in love with Govinda, the Supreme Personality of Godhead, Śrī Kṛṣṇa." (Teachings of Lord Caitanya, Ch 32)