Send Nobles to explore Dungeons and wait for them to return home with any loot they find. When sending Nobles to the dungeons, their level and potential perks coming from their role-unique talents are the stats that help you achieve a higher completion. 

All the potential rewards are displayed if you tap on each dungeon. The further they get and the higher level the Dungeon, the larger the loot!

There are different Dungeon types and tiers, which also means that you will have to level up your Nobles if you want to explore them. The level requirement to explore is displayed if you tap on each Dungeon.

Keep in mind that talents also play a role in this and certain Dungeons require certain Ranger or Explorer talents unlocked, otherwise you cannot explore them at all.