Here is how it works, on this site, you see the Google +1 button and you click it and it opens up an expanded option to add your comments and share it with your circles on Google +:
Then if you see on my Google + profile, the Google+ post shows up right in Google +.
This will save me a ton of time +1'ing my stuff and then posting them to Google + so all my Google + "followers" can be inundated with all my wonderful content on a daily basis.
FYI, Facebook share works pretty much the same way.
Google also added + Snippets within their rich snippets schema to allow publishers to make sure the +1 shares work as best as possible. More on that on the Google Webmaster Blog.
And here is the famous Timothy from Google:
Forum discussion at Google Webmaster Help.