Outside of the SEO world, Google Authorship sounds like books that the folks at Google might be writing. Of course, that's not the case.
Google Authorship is a way for you, as an author of a blog or site content, to attribute your work to your account (and help with fighting content scrapers who take your content and try to make it their own).
Danny Brown shared a Slideshare recently on the subject. It walks you through the setup process for Google Authorship.
If you have a blog and don't have your Google+ account working on your behalf, you're missing out.