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 and project.  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 or project, only the owner can apply Security Rights to that group.

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

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

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

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