Sri Narasimha Jayanti is the appearance day of Lord Narasimha, the half-lion half-man incarnation of Supreme Lord Krishna, who appeared to protect Prahlada from his demoniac father Hiranyakashipu.
Hiranyakashipu received a special benediction from Lord Brahma that he could not be killed by any human being, demigod or animal or any other entities; he could not be killed by any kind of weapons, neither during day nor night. So, the Lord appeared in half-man half-lion form and killed him with His nails at twilight, thus satisfying all the conditions.
Narasimhadeva appeared at dusk on the Shukla Chaturdashi (fourteenth day of the bright fortnight) in the month of Vaishakha (May). Devotees fast till dusk.
You can see our video of Narasimha Deva Festival here-