The "messenger" app that comes with it is possibly the most under-rated feature of not just Google+, but Android in General.
BlackBerry marketed their BlackBerry messenger so much, and as a former owner of a BB, I understand why -- the only problem was that by the time I got rid of my last BB and brought Android, I had only about 2 or 3 friends left still using BBs, so BBM was pretty useless to me. Still though, it had a lot of great features, including group chat and the ability to send pics in the message thread.
Guess what, Google+ Messenger does that as well...and is available to all Android *and* iPhone users with a Google+ account (and maybe BB users too? I don't know). I have a few friends that now use it, and the group message functionality of it is great -- more "instant" and less inbox-congesting than using email, and more intuitive than standard text messaging.
Back to the original question... I admittedly don't use G+ very much, but what I really like about it is combines some of the best features of both Facebook and Twitter, and allows you to determine in what manner you'd prefer to use it. Fb, to me, is all about personal information -- sharing and interacting with specific people you know, and sharing things about yourself...this is probably why I don't really use Facebook at all, because I could really care less about that kind of stuff. Twitter, on the other hand, I've found to be an immensely useful tool, which I use like a news aggregate. If you want to only follow and interact with your friends on twitter, you *could* do that, but if facebook is about interacting with your friends, twitter is all about interacting with strangers, and because of that there's a lot less personal info shared on twitter. I think that Twitter is also the most underutilized and misunderstood (by those who have never used it) tool on the web today. When I check my timeline, for example, I see mostly updates from news sources, updates from beat writers that follow my favorite sports teams, techie sites, and stuff like that. Again, for me, twitter is like the best real-time news aggregate I've ever used.
G+ kinda combines the best of both worlds -- it provides an arena to share personal thoughts and status with (only) your close friends, but also allows you to "follow" anyone publicly (for example, I follow Android Central, and get updates of all their new posts in my feed). If you share anything on G+, you have the option to either share publicly, with only a group of friends, or only 1 person if you want.
The biggest problem with G+ right now is that simply not many folks use it, so it's not as useful as FB or Twitter for either sharing or following...but I'm betting it will get there.
ICS already appears to integrate a lot of G+ features (like contact "circles"), so my guess is that as more folks begin to own ICS devices, the more people will begin to give G+ a shot.
If you're not really into the whole "social" network thing, that's cool, but I figured I'd try to answer your question.