Facebook has been testing Groups for Pages since at least April, when CNET reported that brands like HBO had created Groups tied to their Pages.
There are a couple ways to create a Group for a Page (assuming you are an admin for a Page). On Facebook’s desktop site, there should be a “Groups” tab listed in the left-hand menu. If it’s not there, you can click “Settings,” then “Edit Page,” then “Add a Tab” to add the “Groups” tab.
The “Groups” tab serves multiple purposes. For users, it’s how they will access a Page’s Groups. For the Page Administrator, the “Groups” tab is how they can create and manage their Groups.