Hey! Thank you! I'm glad you enjoyed!
The Quest Stat is for the boss, if you reach the boss with the stat associated to your quest, with a value of 4, 5 or 6, you are allowed to roll an extra d6 against it. So try to keep it high, otherwise the boss battle may be though since you'll be rolling only 1d6.
This is written in the Boss section referred as "quest stat".
Hope it helped!