One of the new features of Blogger.com is the ability to share a post with your Google+ friends, though for you to be able to do this, you must have linked your blog with your Google plus account.
If you have linked your blog to your Google plus account, you will see a Google plus sharing box immediately after publishing a post.
The Google+ share box will contain a snippet of your post that you can share with your circles on Google+. Before sharing the post, you can choose which of your Google+ Circles you would like to share the post with.
You can also share individual posts on Google plus by selecting "Share" right under the posts in your posts list as seen below.
The Google plus sharing box will pop up once you click on the "Share" link.
If you don't want the Share box to be appearing after you publish a post, you can disable it on the “Settings – Posts and Comments” page.
To disable, just set the "Share to Google+" to NO and save the settings.
Feel free to check out this Google Plus Manual.