For instance, page faults should normally be delegated to the operating system that manages the page tables rather than handling it in a higher mode which doesn't know anything about the OS's memory management.  So if page tables are managed in S/HS, you don't want to handle page faults in M mode and you use medeleg to do the delegation.  Similarly, if a guest (VU or VS) gets a page fault then you want to use hedeleg to delegate to the guest OS which is managing VS-stage page tables.

-Paul