Objectives were introduced in version 1.15. You can attempt objectives in the catacombs. Any enabled Objectives will be displayed when the group engages into the catacombs.

Example:
Objectives Enabled: Explore the Maze

When you complete an objective, a reward will be given to your character, usually in the form of a stat bonus.
Stat type bonuses will remain with your character until you reroll or attempt a Master Quest, after which they will be reset, and you will be able to complete them again on your next climb.

I will list the Objectives and more info as time progresses, and as the community discovers their secrets for themselves. Have fun, and good luck!