Book Quests are quests received by reading certain book items that are either bought from city Sages, found in terrain items, or looted from chests. The majority of book quests consist of 9 steps during which you kill some number of creatures and then read the book again for the next step. The reward for completing the quest is experience and a house item version of the book.
A rare few books instead give you 3 separate book quests, each consisting of only 3 kill steps. You receive experience for each quest, but only receive the house item book after completing all 3 quests.