Public groups are usergroups that are open and free to join. Unfortunately, we have no open groups like that at this time. If we get more organized and have more members devoted to the site, we might be able to create public groups in the future.
Now, that vCard thing is pretty much just an information card. It includes things like your email address, name, and other jazz. By default, it's off, so no one can download that information, but they may still view your public profile.
Hope that helped