“Sauti said, ‘Brahma having thus spoken to Vyasa, retired to his own abode. Then Vyasa began to call to mind Ganesa. And Ganesa, obviator of obstacles, ready to fulfil the desires of his votaries, was no sooner thought of, than he repaired to the place where Vyasa was seated. And when he had been saluted, and was seated, Vyasa addressed him thus, ‘O guide of the Ganas! be thou the writer of the Bharata which I have formed in my imagination, and which I am about to repeat.”

In plain words: Sauti, the storyteller, says that after Brahma left, Vyasa thought of Ganesha, the elephant-headed god who removes obstacles. Ganesha came at once. Vyasa greeted him and asked him to write down the story of the Bharatas as Vyasa recited it.