The new +1 button behavior makes it significantly easier to share relevant content with Circles on Google+. A simple click of the +1 button, a brief comment about the content, choose which Circles to share with, and voila!
Previously, I would have copied the link from the article, then switched to Google+ where I would share that link and type in my comment. My old process is more tedious and makes it likely that I will only share things that really seem worthy of the effort. The new method, though, enables me to share with Google+ without giving it a second thought.
Currently, the feature is only available for users registered to experiment with the --sort of the beta before the beta. Expect to see the new and improved +1 button behavior soon, though.