As you explore the map in Genshin Impact you will discover Shrines dotted through the world. The Shrines are relics of an ancient civilization that has been lost. You can find them dotted around the map, and if you interact with them you will be told that you need a Shrine of Depths key to unlock them. If you do manage to get them unlocked, you will find a Luxurious chest inside, filled with loot.
To get a Shrine of Depths key, you will need to finish quests, or complete Abyssal Domains. Shrine of Depths keys can drop as rewards from Archon Quests (the main story), specific NPC quests, world quests, or comissions/daily quests.
You can find the location of all the Shrines in the game on the map below.
Abyssal Domains are dungeons that you can find dotted around the map, and completing them will potentially reward you with a Shrine of Depths key. Many of them will have a rotating set of rewards each day, and will reset daily at 4 AM. We are still trying to track down exactly which in-game activities will reward you with a Shrine of Depths key, and will update this guide when we have it all worked out.
It is also important to note that the Shrines in Mondstadt and Liyue need keys earned from those specific regions to be opened. When you do finally get one open, you will receive an assortment of Primogems, Adventure Rank, Sigils, Weapons and Artifacts.