“Ganesa, upon hearing this address, thus answered, ‘I will become the writer of thy work, provided my pen do not for a moment cease writing.” And Vyasa said unto that divinity, ‘Wherever there be anything thou dost not comprehend, cease to continue writing.’ Ganesa having signified his assent, by repeating the word Om! proceeded to write; and Vyasa began; and by way of diversion, he knit the knots of composition exceeding close; by doing which, he dictated this work according to his engagement.

In plain words: Ganesha agrees to write, but only if Vyasa never makes his pen stop. Vyasa adds his own condition: Ganesha must understand every verse before he writes it. Ganesha says 'Om' to agree. Vyasa then sometimes made verses very tricky on purpose, so he had time to think while Ganesha worked them out.