Holi is fixed to the full moon of Phalguna, the last month of the year in the north Indian reckoning, which places it in late February or March, and it is a two-part observance that popular accounts usually reduce to the second half.
The first night is Holika Dahan, a bonfire. Its narrative is the story of Prahlada, a devotee of Vishnu whose father the demon king ordered him killed; the king's sister Holika, said to be immune to fire, sat in the flames holding the boy, and burned while he was untouched. The bonfire enacts the burning of Holika. The story comes from the Puranic literature, principally the Bhagavata Purana.
The second day is the colour, Rangwali Holi, in which powdered pigment and coloured water are thrown at anyone within reach. Its association is with Krishna and the gopis at Vrindavan, and the tradition in Braj, the region around Mathura and Vrindavan, is the most elaborate in India, running for over a fortnight and including a version at Barsana in which women drive men off with sticks.
The social feature everyone notes, and which the tradition itself notes, is the suspension of ordinary rules. Caste, gender and age distinctions are temporarily set aside, seniors can be doused, and the licence extends to language. Anthropologists have written about it as a ritual of reversal comparable to carnival, and McKim Marriott's account from the 1960s is the standard reference.
The reversal has a well-documented cost: harassment of women under cover of the licence is a recurrent problem and is discussed openly in India.