Radha and Krishna are One, and when Krishna desires to enjoy pleasure, He manifests Himself as Radharani. The spiritual exchange of love between Radha and Krishna is the actual display of the internal pleasure potency of Krishna. Although we speak of “when” Krishna desires, just when He did desire, we cannot say. We only speak in this way because in conditional life we take it that everything has some beginning; however, in the absolute or spiritual life, there is neither beginning nor end. Yet in order to understand that Radha and Krishna are One and that They also become divided, the question “When?” automatically comes to mind. When Krishna desired to enjoy His pleasure potency, He manifested Himself in the separate form of Radharani, and when He wanted to understand Himself through the agency of Radha, He united with Radharani, and that unification is called Lord Chaitanya.
Why did Krishna assume the form of Chaitanya Mahaprabhu? It is explained that Krishna desired to know the glory of Radha’s love. “Why is She so much in love with Me?” Krishna 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 Krishna, as the Supreme should be attracted by anyone’s love. We search after the love of a woman or a man because we are imperfect and lack 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 Krishna, who is full in Himself. Thus Krishna expressed surprise: “Why am I attracted by Radharani? And when Radharani feels My love, what is She actually feeling?” In order to taste the essence of that loving affair, Krishna appeared just as 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 love affairs the moon of Chaitanya Mahaprabhu appeared. Indeed, Chaitanya’s complexion was golden, just like the moon.
Source: A.C. Bhaktivedanta Swami Prabhupada (2012 edition), “Teachings of Lord Chaitanya, The Golden Avatara”, Page 14 & 15