Short version: it's about curation and being able to consume and publish in targeted ways.
The fact I can tune in/out of groups was got me. Everybody is talking about circles as a privacy feature in terms of publishing, but I think the value is two-way.
So I have you Ben in a bunch of circles - friends, colleagues, manchester tech scene, etc. - so you're appearing a lot of places when you choose to publish to the circle or circles I'm in for you, but I have others just in one circle.
If I just want to see what my mates are up to, I can. If I just want to see what Silicon Valley entrepreneurs/technologists are up to, I can. If I want to see what people I know through my work who aren't developers (i.e. pilots, business aviation brokers, my company's clients, etc.) are up to, I can.
It is perhaps the first social media tool that can justifiably be used during work hours and you can prove it's not a waste of time, providing everybody curates and manages their circles properly.
And of course, being able to direct my posts is useful. Being able to post something without my friends/family seeing it (because it's geeky and they'd be bored) is as useful to me as being able to shove stuff under their noses but not have to make everybody else suffer it (e.g. if I were to get a new puppy... :-) ).
I also love the idea of being able to add customers/clients/whoever to a circle and being able to publish material just to them like a business newsletter.
Once the API rolls out, there is going to be some seriously clever crap built on top of this, with the proviso that people manage their circles and use them appropriately. If everybody just publishes to "Public", it'll be just a long-form Twitter.
Anyway, it all just clicked after a little while. I know that's the point, but it took me some mental adjustment to really "get it" and why it's such a powerful model. Technically it's not very complicated to implement either - users HABTM circles which in turn belong_to users (i.e. "owners") - amazed it took so long to be invented with a decent UI!
The point is though, it's not Facebook, it's not Twitter, it's not Buzz, it's not Quora, it's not any of those things: it's all of them, made a little bit smoother and more useful.