Matsyavatara is the 1st among incarnations
Among ten incarnations of Lord Vishnu, who descended to the earth from His heavenly abode to kill demons who disturbed peace and tranquillity of the human beings in the creation and restore the cosmic order, the Matsyavatara is the first and the foremost one.
Matsya Purana and Bhagavata Purana elaborate on the narrative of this avatara, its significance and purpose.
King Manu had renounced the world and did a lot of austerities. Brahma the creator pleased with his austerities granted him the wish to rescue the world at the time of the Pralaya [the great Deluge].
One day Manu was about to offer water as part of his austerities he found a tiny fish in his palm. He was about to throw it away, when the tiny fish pleaded him to protect him from bigger fish. So Manu let it into his kamandala but soon it outgrew his kamandala and had to be transferred to a pot, then to a bigger vessel, then to a pond, then to bigger water resources.
Manu realized that it was not an ordinary fish but Lord Vishnu himself and prayed to the Lord.
Saving world from Pralaya
Lord Vishnu informed him that the time of pralaya is approaching and ordered him to collect samples of all grains, plants and animals and wait for a big ship to arrive. As soon as the ship arrives he had to tie it to the horn of the mammoth fish.
When the pralaya started, Manu did as he was told. He tied the ship to the Great Fish with the help of Vasuki [the serpent] and helped everyone to safety till the deluge is complete.
Somakasura stealing Vedas from Brahma
Meanwhile, Brahma (whose day is equal to one kalpa at the end of which the pralaya takes place) was feeling sleepy and involuntarily took a yawn. Somakasura [also known sometimes as Hayagriva] slipped in and stole the Vedas from the yawning mouth of Brahma and ran away to hide in the deep waters of the ocean.
The Vedas being absolutely necessary for the creation at the beginning of the new kalpa (World or Generation), the Devatas went to Lord Vishnu pleading him to rescue creation by retrieving the Vedas.
Lord Vishnu who had already taken the incarnation of Matsya went to the deep of the ocean killed the demon Somakasura and got back the Vedas just in time for renewal of creation in the new kalpa.
Lord Vishnu - Protector
The myth is significant as it shows Lord Vishnu as the Protector and reinforces the concept of omnipresence of God.
In addition to exemplifying what Krishna, another avatara of Lord Vishnu assures Arjuna in the Bhagavatgita that he would always come to the rescue of the Good whenever the evil seems to take over the creation.
Scientifically speaking, it is also a myth that talks about creation. The aquatic beings like fish were the first to evolve in the long process of evolution.