It was the time of Kalyug. People weren't acting righteously. Soon, Lord Vishnu realized that the time had come. He created a new Brahma from his belly button. It was collectively decided by the Gods that mother earth will be flooded and then Lord Brahma will renovate it again. Please note here that every time a universe is created, it means that a new Brahma is created, who then creates the universe. Likewise, there are other universes as well and other brahmas as well. Lord Vishnu looks after their management.

Lord Vishnu taught the Vedas to Brahma. Vedas were the guidelines that the people in Satyug should follow to live an ideal life and avoid sins. After acquiring the Vedas, Lord Brahma decided to take a break before he started with the creation of the earth because he was tired. However, while he was resting, a horse headed demon named Hyagriv, who was created from the nose of Lord Brahma decided to steal the Vedas.

Guys, please understand the fact that current Vedas are much different than the Vedas of that time. Earlier, Vedas were huge but after Kalyug, Rishi Vyas decided to shorten it so that people can still understand the Vedas despite their less brain capacity in the Kalyug. He even divided the Vedas into four parts, Rigveda, Samveda, Yajurveda and Atharvaveda.

However, before that, the Vedas were in the oral form and whoever had the full knowledge of these Vedas could become invincible. So, due to this, Hyagriv started stealing the knowledge of the Vedas and hid himself in the sea because he wanted to live after the calamity.

Meanwhile, there was this king named Satyavrata who was a great devotee of Lord Vishnu. So, Lord Vishnu decided that Satyavrata will play the role of Manu. So, according to the story in the Matsya Purana, Satyavrata was washing his hands in a river when a small fish swam into his hands and prayed him to save his life. So, Satyavrata took the fish home and placed him in a kamandal (a praying vessel made from the bark of the Kamandalataru tree) which it soon outgrew.

He then moved the fish to a tank, a river and then finally to a sea but to no avail. The fish then revealed himself to be Vishnu and told him that a calamity would occur within seven days that would destroy all life. The fish told Manu that at the end of Kalyug, the mare who lived at the bottom of the ocean would open her mouth to release a poisonous fire. This very fire will burn the whole universe, Gods, constellations and everything. The seven clouds of doomsday would then flood the earth until everything was a single ocean, the cosmic sea.

Therefore, the fish instructed Satyavrata to take all medicinal herbs, all the varieties of seeds, accompanied by the seven sages and other animals. As the time of the flood approached, Manu had told the required creatures about this. As the flood swept over the land, Manu asked Vishnu why mankind had to meet such a deadly fate to which Matsya Vishnu told Manu that he was the only moral man alive and that he would be the father of the future generations of men. Matsya killed Hayagriva and returned the Vedas to Brahma. Then he tied himself to Manu's ark using Vasuki as a rope and protected them from the storm and the floods. When the storms ended and the water subsided, Matsya Vishnu left Manu and the others at the Himalayas, where they could begin human civilization again. Please understand here that the earth was being created when they were away. It was the cosmic sea that they travelled in and not water.

So, this was the story of Matsya avatar. It happened after Kalyug and before the start of Satyug. I hope you guys liked it :)