There was once a demon king by the name of Hiranyakashyapu who won over the entire earth. He was so egoistic that he commanded everybody in his kingdom to worship only him. But to his great disappointment, his own son, Prahlad was an ardent devotee of Deity Narayana (Vishnu) and refused to worship his father.
Hiranyakashyapu tried several ways to get his son to worship him. But all his efforts failed and he ordered his servants to kill Prahlad a number of times but Deity Vishnu rescued him every time. Finally, Hiranyakashyapu turned to his sister Holika. Holika had been blessed by a boon which made her immune to fire. So her brother asked Holika to enter a fire with Prahlad in her lap. The demon king was sure that there was no way Vishnu could save Prahlad from death now!
Holikasat on a pyre and coaxed young Prahlad to sit in her lap. She then ordered her attendants to light the pyre. Legend has it that Holika had to pay the price of her cruelty with her life. Holika was burned to death because her boon was that she would be untouched by fire if she was alone!
Prahlad, who kept chanting the name of Deity Narayana all this while, came out unharmed, as Deity Vishnu had blessed him once again for his unwavering devotion.
Thus, Holi derives its name from the burning of Holika. And, is celebrated as a festival of victory of good over evil.
[Source: https://www.hindujagruti.org]