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. Lord Narasimha out of compassion removes obstacles on the path of devotional service.