Hello,
You inquired in another post (http://www.seomoz.org/q/ideas-needed-for-onsite-seo#post-99529) about this Q&A and why my picture appears next to my SEOmoz results in SERPs.
For SEOmoz, I added a link to my G+ profile page on my author page, and I also added a link from my G+ page to my SEOmoz author page. Now my SEOmoz results show with my picture next to them.
How does this benefit your websites rankings? The only thing I can see it benefiting is the blog the guest post is on??
In short, it does not offer a direct benefit. It is not designed to either. Indirectly, it can offer a benefit.
Let's forget search engines exist for a moment and think about how guest blogging works. You have a niche site on gardening. You would like more readers. You recognize Better Homes & Garden is a popular magazine in your niche. You publish an article in the magazine. In the footer, you mention your website. If your article is well written and helpful, some readers will then want to learn more about you, the author. They may visit your site. Additionally, they may become a bit more familiar with your name and image, so the next time they see it they have an opportunity to recognize you.
This same logic applies to guest blogging as well. If you were to post the same article on the Better Homes and Garden website, all the same logic applies. The only difference is you would have a link to your website. That link offers two additional benefits. First, it is easier for users to click a link after reading an article on a pc then remember the URL after reading the magazine and visiting your website later. Secondly, Google and other search engines recognize the link has value therefore the link may help your rankings.
Now let's loop back to your authorship. Every time you publish an article related to your niche it improves your recognition and therefore your status as an author (assuming the articles are of a quality nature). There may be a slight benefit in this regard recognized by Google. Also, since your image appears in SERP next to your guest blog article, users may later see your image next to another article on your site and then be more likely to click on that result due to the recognition factor.