Destroyed Shrines in The Blood of Dawnwalker are Shrines that have been damaged and are initially unusable. They appear during exploration and need to be restored before they can function as normal Shrines.
Once restored, they can provide the usual Shrine functions, such as fast travel, accessing storage, spending skill points, and managing time. This makes restoring Destroyed Shrines useful because it expands your network of travel and utility locations throughout the world.