What is the real relationship between Radha and Sri Krushna ?

1. Birth

Krushna belonged to the royal dynasty while Radha to an ordinary milkman’s family. Like Sita, She too was born out of a resolve (sankalpa).
2. Special features

Radha is the manifest form of devotion unto Krushna. In response to the question ‘How devoted should one be ?’ the Naradbhaktisutra writes ‘Like the gopis (wives of the cowherds) of Vraj (यथा व्रजगोपिकानाम्‌)’. Krushna Himself sent His great friend Uddhav to the gopis to teach him what devotion meant. The incident goes as follows -

Once to display the devotion of the gopis to others Krushna pretended that He had intense headache which did not respond to any medicine. Then He pronounced, ‘Krushna’s pain will vanish with the application of mud beneath anyone’s feet. However the one giving the mud beneath his feet will die. Proclaim this and then bring the mud which someone gives.’ No one was prepared to give the mud from under his feet.

On entering Gokul when Uddhav asked this question to the first gopi that he met, she replied, “If the mud under my feet will relieve Krushna’s headache then I am even prepared to go to hell.”

The devotion of the gopis is an illustration of ultimate devotion. Radha among them was like a jewel in the crown.
3. Futility of misinterpretation of the Radha-Krushna relationship

Radha’s spiritual love (priti), that is devotion unto Krushna has been misinterpreted as love in the Radha-Krushna relationship. Its futility will be realised if one considers Krushna’s age at that time. When Krushna left Gokul permanently He was only seven years old; thus His relationship with Radha was only during the period when He was three to seven years old.
4. The flute

The sound of the flute means the anahat sound. That sound had maddened all the gopis (wives of the cowherds). So one will realise how highly spiritually evolved they were. When leaving Gokul, Krushna gave His flute to Radha and never played it again. Thus He made sure that She constantly got the spiritual experience of Absoluteness (Purnatva) which is superior to anahat sound.
5. Implied meaning

5.1. ‘Water flows from a higher to a lower level. It is called a stream (dhara). When the letters of the word dhara (धारा) are reversed the word becomes radha (राधा). That stream which flows from below upwards is called radhagati. When it reaches the origin, it gets a spiritual experience of being Radha Herself. Acquisition of this state itself is called “blending into zero” or “sainthood”. In other words Radha and Krushna were one and the same. Krushna had Himself assumed Radha’s form to love Himself. Hence although Radha had merged into Krushna, She continued to worship Him for the sake of guiding the other gopis, that is attitudes. One will think that once a gopi reaches the zenith she will see several Radhas. Those following Radha, that is those seekers following the Path of Devotion will see only one Radha because there is no duality in spiritual love, only non-duality.’ - H.H. Kane Maharaj, Narayangaon

5.2. According to the Tantrik and Vaishnavite sects Rukmini representing the Energy of opulence is one of the two Divine Energies (Shaktis) of Krushna while Radha is the Blissful Energy (Ahladini).

A. The Energy of opulence: ‘When Sudama came to meet Krushna he brought along four handfuls of puffed rice. Even that was borrowed by his wife, from a neighbour. After Krushna had eaten just a pinch of the puffed rice Rukmini snatched it from His hands and said, “We are 16,008 in number. Let us all partake of atleast one grain.” She did this because She knew that if Krushna ate even a pinch, Sudama’s city would turn into gold. So if He were to eat everything then the eight supernatural powers along with the entire wealth from the three regions - earth, nether world and heaven would have to serve Sudama all their lives. So great would be the opulence that he would acquire. Rukmini did this because She was the Energy of opulence rather the deity of wealth, Lakshmi. If a devotee of The Lord has devotion with expectation (sakam) then it is only the Energy of opulence which stops him from acquiring all types of opulence totally.’ - H.H. Kane Maharaj, Narayangaon. In short, the Energy of opulence helps in endowing a devotee having expectation with some opulence while the Blissful Energy imparts the spiritual experience of Bliss to the devotee without expectation (nishkam).

B. The Blissful Energy: Radha was the Blissful Energy. She never intervened when The Lord endowed someone with riches because Her incarnation was meant for spiritual emotion generated from devotion. Hence that spiritual emotion (bhav) is referred to as Radhabhav. The spiritual emotion of Radha (Radhabhav) or Radha refers to the Adnya chakra.The implied meaning behind this is when a worldly person or a Guru merges into Krushna when carrying out worldly transactions or preaching to disciples respectively they descend to the level of the Adnya chakra.

This stream of spiritual emotion progressing from below upwards in other words is the progress of the devotee towards Self-realisation. Radha being Krushna Himself was a devotee who remained absorbed in Bliss. She certainly does not obstruct someone from being gifted with opulence. Even if God were to endow someone with Bliss She would not stop Him because Her Bliss never declines. The moral behind this is that by giving opulence to others it decreases, Bliss does not.

In reality, internally were Rukmini and Radha distinct from each other? Certainly not. But They behaved according to the mission of Krushna’s incarnation. Though They were merged into Krushna They did not become separate because to become separate one needs to have ego. Since The Lord does not have ego His actions (karmas) are referred to as divine play (lila) and the play of man are called actions because of his ego.

5.3. ‘Radha was first created in the Go region (Golok) and then became Krushna’s lover. Later She was born in Vrundavan to the cowherd (gopa), Vrushbhanu and became the idol of the devotees in Vrajamandal. She married a Vaishya (businessman) youth named Shashan; actually it was only Her replica which married him. Keeping Her image in Her physical body Radha left that body and merged Herself into Krushna’s heart in Her primal form.’
6. The divine play of Lord Krushna (rasalila)

The word rasa (रस) has originated from two sources - (रसानां समूह:) means the collection of nine rasas and (रस: उत्‍पद्यते यस्‍मात्‌) means that from which ras is generated. The rasa dance (rasakrida) is a beautiful event in the lives of Krushna and the gopis (wives of the cowherds). During the dance Krushna endowed them with the spiritual experience of non-duality (advait).

Reference: 'Vishnu and His forms', Published by Sanatan Sanstha