Matsya is the first avatara of Vishnu, the fish who warns the Manu Satyavrata of the flood, tows his ark to safety and preserves the seeds of all beings, and in the Puranic tellings also recovers the Vedas from the asura Hayagriva. The flood story is older than the avatara: the Shatapatha Brahmana already tells of Manu and a fish who grows and warns him, and the identification with Vishnu comes later, in the Matsya Purana and the Bhagavata Purana.
Modern Practice
Matsya is invoked at the start of a preservative work - the keeping of a lineage, a text, a seed, a teaching through a flood - and at the beginning of the Dashavatara sequence. The tradition's practice is the keeping of what must not be lost.