Noble chests can be found when hunting Monsters, from Barbarian chests or from specific packages. There are different levels for Noble Chest.
In order to benefit from their rewards, you will need Noble Keys in your inventory. Noble Keys can be obtained from Daily Quest rewards or from specific packages.
From your inventory, select the Noble Chest you wish to open and tap on Synthesize. Every time you synthesize a Noble Chest it will consume 1 Noble key and give you 1 Unlocked Noble Chest of the same level. Simply tap on that unlocked Chest and then on “Use” to collect the reward.