According to Narada purana, the demon kind Hiranyakashipu constantly tried to kill his son Prahlada by various tactics but failed every time. One of the tactic was to ask his sister Holika to sit with Prahlada in a bonfire. She had a boon that no fire can harm her. But this time the devotion of Prahlada towards Lord Narayana worked wonders and Holika was burned alive in the fire, while Prahlada was untouched. The Holi festival derives its name from Holika.
According to some scholars, the festival derives it's name from the parched grains called Holka in Sanskrit. It is used for some rituals like Hawana. The sacred ashes (vibhuti) obtained from this offering is called Bhumi Hari and is smeared on the forehead.