The divine appearance of Srimati Radharani has been elaborately depicted in the Padma Purana. The details as enshrined in the Purana are given here:

King Vrishabhanu was a great devotee of the Divine Mother. One day Sri Radha devi graced him with Her transcendental apparition and told him that she would descend as his daughter on the earth near the village "Ravali'. Overjoyed, the king his wife and other companions reached the village from Vrishbhanupur (Barsana). On the 7th day before full moon in the month of Bhadrapada, in the early hours when it appeared that the entire land was suffused with a golden glow all around Sri Radha Parameshwari descended upon the Earth as a two year girl child.

At that time dried-up trees turned green, stones started emitting melodious notes, the dumb began to talk and the lame climbed hills. All of nature displayed ecstatic symptoms by the influence of the Ahaladini Shakti (the pleasure potency).

Coming to know of the descent of Sri Radharani, the celestial sage Narada went to Barsana and requested Vrishabhanu to give him an opportunity to see the divine child. The king prostrated before the sage and said "Maharshi, due to my good deeds in the past, I am blessed with the presence of Laadli Radharani in my house."

Narada saw the divine child and prostrated before Her golden cradle. By the grace of Sri Radha Narada was immersed in bhava samadhi (state of divine rapture). The great sage extolled Sri Radhaji in beautiful verse.

Oh! Parameswari! You are the 'Sandhini Shakthi' latent in the 'Sachidananda Swaroop' (Lord Krishna).

Oh! The enchantress of Krishna.

Oh! Queen of Vrindavan.

Oh! Rasa Swaroopini, you are the embodiment of Yoga Shakti. You are the controller of 'Maya' You are an ocean of 'Rasa'. Your vision always remains inward. From your majestic tranquil face, inexplicable light of divine ecstasy is emerging.

Oh! Mother! Brahma, Rudra and the like cannot comprehend your Tatva (transcendental nature). You do not appear even in the meditation of great yogis. You are the origin of Icha (desire), Gnana (knowledge) and Kriya (action) shaktis. Oh Mother! All divine incarnations appear from your energy. Oh! Janani! I desire to behold that beautiful divine eternally youthful form which is worshipped by Lord Sri Krishna Himself.  

At that very moment a most enchanting and resplendent form of Kishori Radharani appeared before Naradaji. Beholding the transcendental effulgence of Sri Radha, the Devrishi became unconscious.

Radhaji's sakhis awoke him by giving the charanamrita (water used for feet-washing) of Radhika and they said "Oh! Narada what you have seen is the unique and rare form of Sriji that is worshipped by Sri Krishna." Narada your good fortune has no parallel. Even great gods like Brahma, Rudra, did not have the darshan of this form of Sri Kishori. She is going to disappear soon. Prostrate before Her immediately," advised the sakhis. Narada fell flat at Her feet. The Mother of all Creation disappeared even as he looked on.

Mahamaya divides and distances the Jeeva (individual soul) from God and Yogamaya brings him close to the Lord and unite with Him. Maya is one of the shaktis of Radharani.

The Padma Purana vividly reveals Sri Radha Tatva to the world. A few shlokas here are mentioned along with the purport.Sri Radha Krishna graced Lord Shiva with a vision of Their very rare dual form on the banks of the river Yamuna Lord Krishna says:

Viharamya Naya Nitya Masya Prema Vasi Krutha Imanthu Mathpriyam Vidhi Radhikam Paradevatham

Captivated by Her Love I always roam with Her. Know Her as the Supreme Goddess Radha - the embodiment of Supreme Love.

Yo mameva prapannascha matpriyam na Maheswara Na kadapi sa apnoti mamevam tenu moditam || Tasmat sarvaprayatnena matpriyam saranam vrajet Asritya matpriyam radham mam vasikartumarhasi ||

Oh Maheswara, that Jeeva who is devoted to me without having devotional sentiment for Sri Radha cannot attain me. So with all your effort surrender unto Sri Radha, worship Her and It will captivate me.

Idam rahasyam paramam mayate parikeertitam Tvayapyevam Mahadeva! Gopaneeyam prayatnatah ||

Oh! Mahadeva:I have given you a great divine secret. You should conceal it consciously.

Tvamapyetam samasritya Radhikam mamavallabham japanme yugalam mantra sadatishta..

Taking shelter at the lotus feet of Sri Rahda, meditate on my 'Yugal manthra! (The 'Mantra' of Radha Krishna) Then Sri Krishna gave the maha mantra to Lord Shiva.

Tasam tu madhye ya devi tapta chameekara prabha dyotamana dishah sarva kuryati vidyudujjvala ||

Resplendent in pure golden colour she lights up all directions with Her lightning like luminescence.

Pradhanam ya Bhagawati yaya sarvamidam tatam srushti sthityanta roopa ya vidya vidya trayee para ||

She is pradhana (primordial energy). She is pervasive throughout it. She is its creator, sustainer and the destroyer. She is 'Vidya'. She is Veda Vidya as well.

Svaroopa sakthi roopacha maya roopacha chinmayee Brahma Vishnum Sivadeenam deha karana karanam ||

She is Chinmaya Roopini (embodiment of the conscious principle). She is Yoga Shakthi and Maya Roopini as well. She is the cause of existence of Brahma,Vishnu and Shiva.

Characharam jagatsarvam yanmaya parirambhiram Brindavaneswari namna Radha dhatranu karanat ||

She is Chinmaya Roopini (embodiment of ChitShakthi). She is Yoga Shakti and Maya Roopini as well. She is the cause of existence of Brahma,Vishnu and Shiva.

Tamalingyam vasantam tam muda Brindavaneswaram.

I embrace Her in ecstasy, know that I am Vrindavaneswar.