The core Blog module is probably still the best demonstration of this capability which allows one to add multiple, usually closely related modules to the page.  I've only done this a couple of times, typically when I've needed a "Newest whatever . . ." module which after adding to the page along with the main module can then be moved to another pane or even another page.

When added to a page each module instance receive a unique ModuleId. This is true for modules with multiple definitions as well. They will, however, share the same DesktopModuleId. If you move a module instance to another page, its ModuleId will not change. In fact, ModuleId's are unique across the entire DNN install - that is, across all portals of an install.