To expand a Tome World, you will need to leave the world and then pay up with Pagies to be able to expanded. Expanding it will essentially open up the "other half" and allow you to explore more of the world and even take on the boss of that world. Expanding these are essential to getting all the Quills and Pagies for  Had One's Quill and  From Someone Else's Book respectively. You will get this trophy will you have expanded your last Tome World.