What is the benefit to monster knowledge?

If you go into the Character menu and look under Attributes, then Knowledge, there's entries for all the different monsters you've learned about.

I know you can learn these entries via Books (level 3/3 knowledge right away) or by killing enough monsters (gradually increases to 3/3).

What I don't know is the value or benefit to this knowledge. Increased damage to those enemies? Increased drops from those enemies (and if so, is that required for certain special craft components) ? Is it just the advice to the player (like don't try to poison Endregas) ?

Certain contract quests require a specific amount of knowledge before you're allowed to complete them. From that, you'll receive rewards/experience once you turn in these contract quests.

And, as you mentioned, reading the books allows you to obtain the knowledge more quickly than killing a large number of that specific species. You'll also receive some helpful advice like which sword or spell works best with that specific monster.