So what is this Google+ thing?
I've got an invite from a former student to join Google+ social network. Yes, I'd say it is a social network which, as Buzz was an attempt to mimic Twitter, tries to mimic Facebook (others may use a more agressive term).
I like the idea of having a way to create more categories than just the "friend" relationship of Facebook and the fact that this categories (they call circles) are not closed but you are free to open as many as you want. I like the idea of this circles to be able to intersect. For example you may have a coworker that happens to be a friend too, so you can have her in both circles (work + friends).
Android Google+ application includes a cool feature of automatically uploading pictures taken with your cellphone (and videos). Ok, maybe the latter may deplete your battery quickly, but you have the choice of limiting when uploads may or may not happen.
The number of invites you have initially is not high, but as soon as you start adding people to your circles you get more invites so I'd say the growth of the network is not very limited at the moment.
As a user that started trying out Buzz and later giving up I am not certain at the moment on what the future will bring to this new service. On the graphical design & GUI side I'd say that Google+ seems to require much more screen real state that Facebook.
Google+ has the big advantage of good integration with some other Google services like Picasa and Gmail (and I guess some other I have yet to discover).