Lord Narasimha is one of the main incarnations of Lord Vishnu. Lord Narasimha was half-human and half-lion. He killed Hiranyakashyap in this form.
According to Hindu mythology, there was a saint named Kashyap in ancient times who had a wife named, Diti. He had two sons who were known as Harinyaksha and Hiranyakashipu. Lord Vishnu killed Harinyaksha to protect the earth and mankind. Hiranyakashipu could not bear the death of his brother and wanted to take revenge.
He offered austerities and impressed Lord Brahma who appeared and blessed him. After taking Lord Brahma’s blessings, Hiranyakashipu established his rule in all Lokas. He even started ruling the heavens. All the Devas were helpless and could not do anything about Hiranyakashipu’s atrocities.
In the meantime, his wife Kayadhu gave birth to a son who was named, Prahalad. This child did not resemble any demons and was totally devoted to Lord Narayana. Hiranyakashipu tried many different ways to distract Prahalad from Lord Narayana and to make him a demon. All his attempts failed and Prahalad was devoted even more towards Lord Narayana.
Due to Lord Vishnu’s blessings, Prahalad was always saved from Hiranyakashipu’s atrocities. Once, Hiranyakashipu tried to burn Prahalad. He made Prahalad sit over his sister’s (Holika) lap in fire. Holika was blessed with a boon that she could not burn in fire. But, with Prahalad sitting in her lap, Holika was burnt alive and nothing happened to Prahalad.
After Seeing this, Hiranyakashipu was very angry. Hiranyakashipu started worshipping Lord Vishnu. He asked Prahalad about his God. He asked his God to appear in front of him. Prahalad replied by saying that the Lord was present everywhere and resided in everything.
Listening to this, Hiranyakashipu asked Prahalad is his Lord resided in a pillar to which Prahalad replied, yes. Listening to this, Hiranyakashipu attacked the pillar and Lord Narasimha appeared in front of him. Lord Narasimha held him on his legs and killed him by cutting his chest with his nails.
Lord Narasimha blessed Prahalad by saying that everyone who would fast on this day would be blessed and would be relieved from all problems. Hence, this day is celebrated as Narasimha Jayanti.