Groups can be linked together into a federated hierarchy called a network. Groups within a network share data according to their place in the hierarchy. Networks are perfect for federated organizations, organizations with local chapters, field campaigns, and similar structures.
For example, let's say your group named Progressives International is set as the top group in a new network. You can then create other groups and designate them as children of Progressives International or any other group in the network. You could add Progressives America underneath Progressives International, and then Progressives New York and Progressives Montana as children of Progressives America. When an activist takes action on a page sponsored by Progressives Montana, all the groups up the chain will get a copy of that data, which in this case means Progressives Montata, Progressives America, and Progressives International. (But not Progressives New York, as it's a sibling of Progressives Montana, not a parent.) Each group in a network maintains its own unsubscribe option, so activists unsubscribing from Progressives Montana will not be unsubscribed from Progressives America or Progressives International.
Once in a network, various things can be syndicated from parents to children, allowing you to campaign with your groups. For example, tags and custom fields/questions can be syndicated to children, allowing you to keep data organized throughout the network. Content can be syndicated as well in the form of emails and actions that children can then publish and/or send to their lists under their names. More information about syndication is available here.
In this way, complex federated structures can be built. Beyond the data sharing described above, networks offer special targeting options (ex: you can target email to people who subscribed via other groups) and administrator permission inheritance (ex: administrators on parent groups are automatically administrators on children, with the same permissions).