What's the benefit of using books during correspondence games? I'm playing daily games on chess.com and read that it's officially allowed to use books or databases during the game.

My question is: How does it help me getting better (if it's the purpose of this allowance) to use theory sources in daily games?
What you get from the books/databases during your correspondece games is the same as what you get when you read them generally. You can make use of


Opening lines, which become more important as the games get slower and slower
Tactics, which you may encounter during your games
Positional concepts and maneuvers, which play the most important part of a correspondence game
Endgames, though usually tablebases (7-man) are allowed in correspondence games.


All of these (not including tablebases) are allowed because they are simply undiscoverable in a cheating investigation (for example, you can expect perfect opening play from any player), as well as to help you, as you stated.