In A Sentence:
If Twitter and Facebook had a baby, and that baby was much prettier than Facebook but not nearly as cool as Twitter.
In A Few More Sentences:
There's a child-like joy to the actual experience of setting up google+: you drag people into circles, and if you're particularly inclined (I am so inclined) then you can imagine you're creating your own version of Dante's Inferno (yes, I am aware how sinister it is that I am sending all my friends/acquaintances to Hell. Rest assured, other contacts have created far less family-friendly monikers for their circles).
But I digress.
The most important thing here is that G+ is providing a real competitor to Facebook. We were this close to total monopolic consolidation on the Internet: Google as the only search, Facebook as the only "friends" sharing system*, Amazon as the books-opoly, and so on. It may not seem that Google going up against Facebook is the biggest shake-up in online power, but we all know that competition is what leads to progress, to better consumer experiences, to better products.
While I feel that tech savvy (particularly Internet savvy) people are going to latch on to the new service, I think it poses problems for more average users (I partially consider this a positive. For instance, your grandma won't be using google plus). Setting up a profile took a few steps too many for my liking. The often touted privacy features felt removed from all the other account settings (they were in no way obvious), and even simple settings for key G+ features like +1 required leaving the G+ interface and moving back into the main Google account settings.
But what is it for? Twitter took a long time to reach critical mass, because it's added advantage wasn't clear for a very long time; people thought it was just a streamlined Facebook wall for a long time. Google has already proven itself untrustworthy when it comes to protecting dissidents when government push comes to court-ordered shove. I suspect we'll learn more about G+ utility when the business pages come out later in the year.
A Few Suggestions to Make Google Plus Better:
Allow the creation of Venn Diagrams, so you can see how your networks interact (this isn't actually useful, but it sure would be fun. I can see the rom-com now: "The Man at the Center of my Googleverse").
Make it easier to find friends. Specifically, allow imports from twitter. Right now, if people don't have a google mail account, you can't search for them (and sometimes you can't find them even if you do).
Why isn't G+ integrated into Google Reader? I would enjoy +1-ing interesting articles, BUT I CANNOT.
That image at the top? It apparently inspired the whole project. Google had it emblazoned across the walls on the fourth floor of their offices.
*I'm not including twitter in this because it really is a tool, not a destination. It enables communication, unprecendented activism, and lightning speed information sharing. It's simplicity and basic use is its best recommendation. It's not competing with Google+.