Lord Shiva told Parvati that any creature who listens the story, would become immortal, so this story should be narrated only in a solitude place. Thus, Lord Shiva decided to narrate the story inside the Cave so that nobody except the Parvati could listen it.
Parvati started listening the story as Lord Shiva began narrating significance of Amar Katha and she nodded time to time. After sometimes, she got tired and fell asleep and parrot chick started nodding instead of Parvati. When Lord Shiva finished narrating the story, he looked at Parvati and saw her at asleep. He woke up Parvati and asked her when she fell on asleep. Parvati told that she fell on asleep when the story was halfway through. Lord Shiva asked, then who was the one listening and nodding throughout the entire story after you fell on asleep? Parvati said that she did not know anything about that. Upon hearing that, the parrot chick told that it was he who listened the story and nodded after Parvati fell on asleep. After knowing this, Lord Shiva became very furious and tried to kill the parrot. Afraid parrot fled from the scene and Lord Shiva followed it. Eventually, the parrot reached in the hermitage of Vedvyash Rishi. The parrot entered inside the body of wife of Rishi Vedvyash when she opened her mouth. Thus, Lord Shiva could not kill the parrot.
Many years later, she gave a birth to a divine baby whose face looked like a parrot. Thus, he was named Shuka Dev. Since he had listened the entire Amar Katha, he became very intelligent .
( source - google)