The Mastery Books are used for the 4th job skills. When you get a skill at the 4th job and say the max level for it is 10, you will need to use a Mastery Book to increase its level. So if you end up using a Level 20 Mastery Book and it succeeds, that means that the skill that had a max level of 10 now has a max level of 20, which means you can increase that skill now to level 20, instead of 10.
Note that sometimes the Mastery Books can fail, there are 2 types, one with a 50% chance to succeed and another with a 70% chance to succeed. If it fails, you can just get another book and try again.
