Lord Chaitanya is none other than the Supreme Personality of Godhead, Lord Krishna Himself. The Supreme Personality of Godhead, Sri Krishna, advented Himself as Lord Caitanya Mahaprabhu, appearing in Sridhama Mayapura in the city of Navadvipa, Bengal in the year 1407 AD. Sri Krishna Caitanya manifested his divine mercy in Kali Yuga by delivering the Hare Krishna maha mantra and thereby saving the most fallen souls.
The divine appearance of Sri Krishna Caitanya Mahaprabhu is celebrated on the full moon of the month of Phalguna (February-March). This is the most auspicious day for all Gaudiya Vaisnavas. He appeared as the son of Jagannath Mishra and Srimati Saci devi.
Srimati Radharani becomes greatly depressed when Krishna is not around. Krishna is unable to understand the reason behind this. In order to do so, He incarnates as Lord Chaitanya. Thus, Lord Chaitanya is the incarnation of Lord Krishna in the form of a devotee and with the bhava(mood) of Srimati Radharani.