The story Ras Lila stages comes from the tenth book of the Bhagavata Purana, elaborated in the twelfth century poem Gita Govinda: on an autumn night, Krishna plays his flute and draws the gopis, the cowherd women of Braj, out of their homes to dance with him in the forest by the Yamuna river. When each gopi wishes she alone had Krishna beside her, he multiplies himself so every one dances with her own Krishna in a great circle, the rasa mandal, an image devotees read as an allegory of the soul's relationship with the divine rather than ordinary romantic attachment. That reading separates devotional performance from spectacle in the tradition's own understanding of itself.
When the tradition took its present shape is disputed. Wikipedia's own account credits its beginning to the saint Uddhavaghamanda Devacharya in the early fifteenth century, at Vamshivata in Vrindavan. Scholarship more commonly dates the developed Braj rasa lila later, to the sixteenth century, crediting Narayan Bhatta, who settled in Braj in 1535 and wove rasa lila into the pilgrimage circuit, with further growth under Vallabhacharya and his son Vitthalnath. The accounts disagree by over a century and no founding text survives to settle which is right.
Ras Lila is often confused with two neighbors. It is distinct from Ramlila, the autumn cycle dramatizing Rama's story from the Ramayana, a related but textually separate tradition. And it is distinct from the Manipuri Sankirtana inscribed on UNESCO's Representative List of the Intangible Cultural Heritage of Humanity in 2013: that inscription is defined around Sankirtana's own singing, drumming and dancing, and while the Manipuri Raslila alongside it shaped Manipuri dance, neither its title nor text names or covers the Braj tradition described here.