Narsimha is the fourth incarnation of it Lord Vishnu where he appeared as a man-lion that is the face was like a lion and the trunk was like a man. He had killed demon Hiranyakashipu on this day. All Lord Vishnu devotees also observe fast on this day.
The purpose of Narasimha Jayanti is to remove adharm and to follow the path of dharam. Dharam is to perform correct deeds and not harm anyone.
It is a very auspicious day to perform Lakshmi Narasimha Homa on this particular day.