To import groups from other site, you must have a common owner for both sites and also you would need to have import groups feature enabled. You can enable this feature from Site Admin->Site Details->Features.
Step 1: Open the groups tab. And if you are the site owner you would see a Import My Groups button
Step 2: You would see list of groups where you are an admin and which are present in other sites you own. Select the ones which you want to add to the current site and click Select & Close
Step 3: Start using the newly imported group. If you are viewing the group overview page on the source site (where group was originally created), you can see the sites where the group is linked to. And you can click on the delete icon to remove the link.
The imported groups can be joined by the users of the site where its imported, just like a regular group, depending on the Membership Type setting of the group.