The Narasimha (man-lion) form was assumed by Vishnu for the destruction of the demon Hiranyakasipu, a powerful devil that posed as God himself and prohibited the worship of Lord Vishnu throughout the fourteen worlds.
But Hiranyakasipu’s son Prahlad was a persecuted devotee of Vishnu and this deity, to deliver the son from his father, assumed the form of Narasimha and killed Hiranyakasipu.
The man-lion form was chosen as the demon had obtained a boon by which he could be destroyed by neither man nor beast.