Every group has an owner.  Groups created under Server Settings -> Groups will have "Global" as the owner.  Global groups have "Admins can use this group" for every repository.  Groups created under Source Control Repositories -> Individual Repository -> Groups will have that particular repository as the owner.

By default, if a group is owned by a particular repository, only the owner can apply Security Rights to that group.

Sharing a group among repositories allows the group to be reused, rather than setting up the same group multiple times for different repositories.  Administrators of the repository that owns the group can apply one of the following share levels for other repositories:

Admins of the other repository will not be able to see this group.

Allows Admins of the other repository to apply access/folder security settings on this group.

Allows Admins of the other repository to set access/folder security settings on this group.  Admins of other repositories can also change the group members and group name.