A book of knowledge is the reward from the Surprise Exam random event. It grants players experience equivalent to their level in a skill times 15. Compared with a genie lamp, which only gives the experience equal to the level times 10, the book of knowledge is 50% more potent. Many people use this kind of book to level up skills that are time-consuming or expensive to level up, such as Runecraft, Prayer, Construction, Herblore, Farming, or Slayer.
If you try to bank it, you will receive the message "A magical force prevents you from banking this item!".
If a player has a book of knowledge in their inventory, it is very unlikely, but not impossible for a player to receive the Surprise Exam random event. However, the player will only retain one book of knowledge and will instead receive another common reward from random events, such as an uncut gem.
If no inventory space is available, the book will be left on floor. But once it is picked up it is impossible to put it down again.
When it comes to skill pures, the Book of Knowledge's most common use is, along with the genie lamp, to acquire Slayer Experience.
For an exhaustive list of all known sources for this item, see here