On this page of the Genshin Impact guide you will find out what Shrines of Depths are, where to find them, how to open them and what you will receive for opening them.
While exploring the world of the game, you will encounter large shrines, sometimes blue, other times light brown. The color varies from region to region. If it is a region corresponding to Ameno element, it will be blue, if Geo, light brown. To open Shrines of Depths, one must have a key corresponding to the shrine. For Geo, it will be Liyue Shrine of Depths Key, for Ameno, Mondstadt Shrine of Depths Key.
Keys are won in various ways, for example as a reward for completing certain tasks or clearing certain dungeons. If you don't know where to get them, go to the description of the item and click the button corresponding to more information on the subject. Once you open the Shrines of Depths, you'll find a box there. As for opening prizes, you will encounter 10x Ameno/Geo Sigil, 40 Primogems, 60 Adventure Rank EXP and random weapons or artifacts.