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.
Matsya, the fish, appeared in the Satya Yuga. The Fish Incarnation is the first incarnation of Vishnu. Lord Vishnu takes the form of a fish to take a king to the new world along with one of every single species of plants and animals from the world's largest cyclone. What we live in now is the new world, where the Lord traveled, carrying everything from the old, destroyed world.