Treasures are side rewards of quests. Even if your quest objective is complete, you can search the map for treasures, as they may include helpful materials and equipment, before returning to the Quest city.
Gameplay[]
Treasures are guarded by Treasure Guardians (with the exception of the first tutorial quest) and come in three varities (Lightly Guarded Campfire, Moderately Guarded Hut, Heavily Guarded Camp) each one rewarding more Treasure Chests than the previous but having more guardians. The Guardians must be defeated before you can loot the Treasure.
There are some repeatable quests that requires you to defeat guardians under a time challenge.