Hiranyakashipu is the king of demons, and he had been granted a boon by Brahma, which made it almost impossible for him to be killed. The boon was due to his long penance, after which he had demanded that he not be killed "during day or night; inside the home or outside, not on earth or on sky; neither by a man nor an animal; neither by astra nor by shastra". Consequently, he grew arrogant, and attacked the Heavens and the Earth. He demanded that people stop worshipping gods and start praying to him.
Despite this, Hiranyakashipu's own son, Prahlada, was a devotee of Lord Vishnu. In spite of several threats from Hiranyakashipu, Prahlada continued offering prayers to Lord Vishnu. He was poisoned but the poison turned to nectar in his mouth. He was ordered to be trampled by elephants yet remained unharmed. He was put in a room with hungry, poisonous snakes and survived. All of Hiranyakashipu's attempts to kill his son failed. Finally, he ordered young Prahlada to sit on a pyre on the lap of his sister, Holika, who could not die by fire by virtue of a shawl which would prevent fire affecting the person wearing it. Prahlada readily accepted his father's orders, and prayed to Vishnu to keep him safe. When the fire started, everyone watched in amazement as the shawl flew from Holika, who then was burnt to death, while Prahlada survived unharmed, after the shawl moved to cover him. The burning of Holika is celebrated as Holi.
Later Lord Vishnu came in the form of a Narasimha (who is half-man and half-lion) and killed Hiranyakashipu at dusk (which was neither day nor night), on the steps of the porch of his house (which was neither inside the house nor outside) by restraining him on his lap (which is neither in the sky nor on the earth) and mauling him with his claws (which are neither astra nor shastra).
In Vrindavan and Mathura, where Lord Krishna grew up, the festival is celebrated for 16 days (until Rangpanchmi in commemoration of the divine love of Radha for Krishna). Lord Krishna is believed to have popularized the festival by playing pranks on the gopis here. Krishna is believed to have complained to his mother about the contrast between his dark colour and his consort Radha's fair colour. Krishna's mother decided to apply colour to Radha's face. The celebrations officially usher in spring, the celebrated season of love.