Meaning of admin:/// in a URL

Solution 1:

admin:/// is in this case a URI Scheme or Web Protocol, handled by some program installed on the computer.

Wikipedia lists this scheme in its page of List of URI schemes:

Scheme Purpose Defined by General format
admin URL scheme in the GNOME desktop environment to access file(s) with administrative permissions with GUI applications in a safer way, instead of the insecure-considered sudo, gksu & gksudo. GNOME Virtual file system admin://<path>/<to>/<file>
example: gedit admin://etc/default/grub