Matsya is the fish avatar in the ten primary avatars of Hindu god Vishnu. Matsya is described to have rescued Manu and earthly existence from a great deluge.
The Bhagavata Purana presents a modified version for the Matsya mythology. The story is presented through a character named Badarayani. At the end of a kalpa, as the world dissolved and was overwhelmed by a flooding ocean, the demon Hayagriva steals the Vedas from sleepy Brahma. Vishnu takes the avatar of saphari fish, dives down to locate the Vedas and the demon, and recovers the Vedas from the ocean -Wikepedia
What exactly does Matsya Avatara symbolizes?
Scritptures are about seven stage muscle tone based thinking. The first five stages are symbolized by Panchamahabhuta.
In Matsya Avatar it is the water of flexibility that floods the land of Discipline.
Vishnu is the Hindu Preserver god. He keeps our life between a lower limit called Positive (urge to acheive) attitude and an upper limit called Negative (satisfaction) attitudes. If Negative attitude symbolized by land is missing we can’t know our status and Vishnu can’t function as Preserver. Vishnu takes us to an activity (island) that has a Negative attitude, and we can start a new life, using that as the starting point.
The Naoh’s ark story of the Bible too is a similar story.
A similar story exists in the Epic of Gilgemish also.
The flood stories are all allegorically about how to start a discplined life after leading a wanton life.