Book burn is referring to Grounds of Valor (usually abbreviated GoV). Check out the wiki page here
for detailed information, but I'll give you a quick rundown. You select a training regime from the book, and it tells you to kill certain enemies. You then kill those enemies, and when you've completed the regime you will get exp. Now, the best part about GoV is that the exp reward increases each time you complete the regime, so you can do it over and over again and keep getting more exp. That's the idea behind the book burns. Get an alliance of people together to churn through regimes (called pages when you select them from the book), and you start getting exp very quickly. The amount of exp from the monsters themselves is tiny, but doesn't matter because page exp is unaffected by the number of people in the party.
Formerly of Lakshmi, now in Asura