In Hindu mythology, there are four historical eras, yugas, that repeat in a cycle; the first of these is the Satya Yuga, followed by the Treta Yuga, the Dvapara Yuga, and, finally, the Kali Yuga. We are presently in a Kali Yuga that started in 3102 BC. The story of the picture above takes place at the end of the most recent Staya Yuga, about 2.2 million years ago, according to one reckoning (Wikipedia). Now, each yuga is but a single day for Brahma, the Hindu creator god, and at the end of each one, he sleeps—and when he sleeps, he stops creating and thus the universe ceases to exist until he wakes.
The version of the story in this image, as far as I can tell, is told in the Agni Purana, a long and eclectic medieval encyclopedia covering a vast array of topics. What follows is an edited version of this summary:
The Satya Yuga was about to end and a great flood was to come and destroy all the life on earth to start afresh for the next yuga. After a day full of creation, Lord Brahma was tired. He wanted to go to sleep and was soon snoring loudly.
While Lord Brahma was sleeping an asura—a demon—named Hayagriva emerged from Brahma’s nose. With Brahma asleep, Hayagriva realized that it was the right time to take in all the knowledge of the Vedas—the ancient Hindu scared texts. Hayagriva concentrated and soon absorbed the knowledge in the Vedas. He then hid deep inside the ocean, thinking that nobody would find him there.
Lord Vishnu saw this and was worried. If the Vedas were stolen by the asura, the knowledge of the Vedas could not be passed on to the next yuga. Vishnu is the God of Preservation; whenever the earth is in danger and when evil threatens to overpower good, Lord Vishnu descends from the heaven to incarnate on the earth.
At the same time, there was a king named Manu. He was a staunch devotee of Lord Vishnu. His greatest desire was to see Lord Vishnu with his own eyes. For this he performed severe penance for thousands of years. Wondering what to do, Lord Vishnu looked at Manu performing penance and smiled, realizing that he could achieve much more than just save the Vedas.
The next morning, Manu went to the river to begin his prayers. He took the water in his hands and held it high above his head and offered it to the Lord Vishnu to mark the beginning of his prayer. He was about to pour the water into the river, when he heard a tiny voice from his hands. “O great king! Please do not put me back in the river!”
Surprised Manu stared at his hands. In the palms of his hands was a tiny fish, squirming. The fish looked at Manu, pleading, “Please do not put me back in the water. There are so many bigger fishes in the water, they will eat me. Please, O great king!”
Manu looked at the tiny fish with pity. As a king it was his duty to protect anybody who came to him for help. The king readily agreed and put the fish inside a small jug called a kamandalam. He then finished his penance and went home for the night. He had left the fish inside the kamandalam, knowing that the fish would be safe inside. He woke up next morning hearing a strong voice, “O king…Help me…Your kamandalam is stifling me. I cannot breath in here…” Surprised Manu looked at the kamandalam, only to find a big fish staring at him from the top of it.
Overcoming his surprise, Manu ran inside his house to get a bigger vessel. The fish gulped a few breaths and said softly, “Thank you, kind king.” Manu smiled and was about to walk out the home to begin his morning prayers, when he heard an even more powerful voice: “King, this vessel in too small for me. Please get me another one.” Manu blankly stared as the fish stared out of the vessel he had just gotten. The fish was again struggling for breath. Manu brought the biggest vessel in his house and threw the fish inside it. The fish thanked him and after checking that the vessel was big enough for the fish, still puzzled, was about to walk out of the house, when he heard a strong voic:, “I am sorry this vessel is also not sufficient for me, king.” Manu stared in disbelief as he saw the huge fish stare out of the big vessel. However, realizing that this was not the time for questions, he carried the fish and ran to the river, where he threw it in.
The fish gulped a few breaths inside water. “Thank you, king. You have protected me. But please don’t leave me here. I am afraid the other bigger fishes may eat me!” Manu began to get suspicious, but he was a king. He could not just stop protecting someone who had come to him for help. He stared at the fish for long and before his very eyes saw the fish getting larger and larger, till it had covered up the entire river.
The same routine followed again. Manu carried the fish from one river to another river, but the fish kept getting bigger. Finally, he dropped the fish inside the ocean, only to find that the fish grown to full one side of the ocean. Looking at gigantic fish, a sudden flash came to Manu. He bowed before the fish, “Narayana, you are Narayana, my Lord.”
The fish smiled, “You wanted to see me and here I have come.” Manu stared with tears in his eyes, as a huge horn grew on the head of the fish.
“My Lord, you have granted me my only desire. I want nothing more. What do you want me to do now?” Manu said prostrating before the fish.
“Manu, the yuga is about to end in seven days. There will be a great flood and all living things on the earth will perish. I want you to build a boat. Take the seeds of all plants and the seven sages along with their families. Take them all on the boat.”
Manu nodded. The fish continued. “Don’t forget to bring Vasuki, the snake God also.” Manu nodded again as he watched the fish tear through the ocean to the other side.
One half of the fish’s work completed, the fish went to the other side to complete the other reason for the incarnation. On the other end of the ocean, the fish saw Hayagriva guarding the Vedas. Seeing the huge fish, Hayagriva was terrified. What a huge fish! However no sooner than he had thought this, the fish attacked him. The fish was so huge, that a single push sent the asura reeling. Still dazed, Hayagriva tried fighting the fish, but the fish was huge and powerful.
After a brief and futile struggle, the asura was dead. Once the asura was dead, the vedas imbibed by him went back to Lord Brahma, who was still asleep.
On the other side of the ocean Manu was building his boat. He had also brought the seven sages. Soon there were torrential rains which washed away everything. The water level kept increasing and very soon there was a flood. The boat wobbled and many times was about to capsize, but Manu and that others were steadfast in their belief that Lord Vishnu would protect them.
Soon the fish came as promised, “Manu, use Vasuki as a rope to tie my horn to the ship” It bellowed loudly, above the roar of the rain. Once the fish was tied to the ship, the fish guided the ship in sea and kept the ship safe while the storm raged outside. The fish taught the Vedas to Manu and the others during the voyage. After the storm abated and everything was washed away, the fish deposited the boat at Mount Himavan for the people there to continue the new yuga.
The image, found here, is undated.