The main screen of Facebook Groups displays all the groups you belong to. From there, you can access any of them, see posts from other users, add comments, etc. Most interestingly, you'll also be notified of everything that happens in each group.
The other tabs in Facebook Groups let you quickly access all the news from each groups (and from here you can see comments from other Facebook users) or see suggestions for other groups that might interest you. From another tab, you'll be able to straightforwardly create new groups.
Facebook Groups is a very useful app for anyone who uses Facebook regularly. Nowadays, everyone's in at least two or three groups, and Facebook Groups offers a nice interface from which you can manage them.