Dashavatara refers to the ten principal Avatars. In Vaishnava philosophy, an Avatar most commonly refers to the 'descent' and dasa refers to 'ten' in number. The ten most famous incarnations of Vishnu or sometimes Krishna are collectively known as the Dashavatara. This list is included in the Garuda Purana (1.86.10-11) and denotes those avatars most prominent in terms of their influence on human society.
Narasimha, the half-man/half-lion appeared in the Satya Yuga. The Man-Lion Incarnation is the fourth incarnation of Vishnu. When the demon Hiranyakashipu acquired a boon from Brahma, which gave him inordinate power, Lord Vishnu appeared in the form of half-man/half-lion, having a human-like torso and a lower body, but with a lion-like face and claws.