Matsya means fish. The Matsya Purana is not all based on the life story of a fish, and not just any fish. Besides, it deals with various other subjects too. For all that, in some chapters it is a fish that speaks, a fish with a horn.
The Matsya Purana describes the fish incarnation of Vishnu, and this story is simplified:
One day an ancient king noticed a small fish in the palm of his hand. He put it in a water pot. In just one day the fish grew too big for it. The same thing happened when the king put the fish in a jar, and later a well, a pond, a river, and the ocean.
When the fish filled the entire ocean, the perplexed king did not know what to do, and asked the fisk.
The fish said: "Soon the earth will be submerged into the water. Look here, here is a boat. It is made of the Vedas. Place living beings on it. When it is rocked by furious winds, then fasten the boat to my horn. When the storm is over, you will have saved the creatures." (2007, 2-4)
Here is an interpretation:
The fish is the symbol of the Cosmic Egg of the Creator. Here the Creator himself is the fish. (2007, xxx)
Sages in the Naimisa forest asked Suta again to tell how Vishnu took the form of a fish.
Suta said, "In earlier times, Manu, the proficient son of the Sun, got the best success in yoga. The Creator got pleased with Manu and asked him to ask God for a boon."
Manu: "At at the time of every deluge, I should be able to protect the entire mobile and immobile creatures."
The Creator: "Be it so." (2007, 2-3)