Lord Narasimha is the fourth incarnation of Lord Maha Vishnu who incarnated to kill Demon Hiranyakashyapu and to save his devotee Prahlada. In this avatar, Lord Vishnu appeared in the Half lion-Half man form.
According to Bhagavata Purana, demon Hiranyakashipu performed vigourous tapa(austerity) to please Lord Brahma for taking revenge on the Devas as his brother Hiranyaksha was killed by Lord Vishnu,and to conquer the universe. After performing tapa for a long time the demon Hiranyakashipu got a boon from Brahma such that He cannot be killed neither by a human being nor by an animal,neither by a demon nor by a God,not with a weapon, neither in day nor in the night,neither inside nor outside. So after getting a boon he returned to his kingdom and began to conquer the Earth. He also defeated the demigods. I the meantime, He got a child named Prahlada.The demon Hiranyakashapu,wished that his son learnt the asura vidyas and become a powerfull king of asuras. He thus sent him to a guru,and prahlada refused to leave Lord Vishnu's Devotion.
Demon Hiranyakashipu, with the pride of his boon and in a thought of conquering The whole Earth, declared himself as God and stopped all Vishnu poojas(worships). Prahlada told his father that Lord Vishnu is the only god and he would not accept his father(i.e. Hiranyakashipu) as a God. Hiranyakashipu was extrmely enraged and ordered his servants to kill Prahlada.The servants threw Prahlada from top of mountains,and in to the sea,in to snakes dungeon and also into the fire.But Prahlada prayed to Lord Vishnu and thus He was protected. The servants took him to the Demon Hiranyakashipu and He asked Prahlada that where is Lord Vishnu present, in order to fight with him. Prahlada replied that He is present every where. He asked Prahlada, "Is your Lord Vishnu present in this pillar". Prahlada replied "Yes, He is present in this pillar". The Demon Hiranyakashapu took his mace and was about to beat the pillar to find Lord Vishnu and fight with him.At that moment Lord Vishnu emerged from the pillar as Lord Narsimha. A fierce fight unsued between Lord Narsimha and Hiranyakashipu. Finally, Hiranyakashipu was completely tired and exhausted.
Then at dusk, Lord Narismha took Demon Hiranyakashipu on his thighs and sat at the exit of the court, which was neither inside nor outside. It was the time of dusk – neither day nor night. With his nails He opened Hiranyakashipu's stomach (which is not a weapon) and killed him. In this way, He protected His devotee -Prahlada Maharaja.