Sorry, I'm new, so I have a lot of silly questions!

What do the book items do? Are they just items to buy and sell for quests, or can you read them to your pets to increase their "intelligence", or what?

yup, reading books to your pets increases their intelligence, which affects which jobs & promotions they can get. every 16 books your pet reads also increases their alchemy points (AP) which determines which scrolls they can make and use in battle.

(or, well, to be more specific and confusing, it's every 16th point of intelligence gained regardless of source, but a book must be read to increment the AP. yes, i know, don't worry about it.)