A link share, or embedded link, is when you create a Google+ post and paste a URL into the "Link" field (versus a photo or video). If your featured image is wide enough (assume 570px or more) you'll get this beautiful new look, with the title, business page name (for some), and meta description written underneath.
Google+ has now joined the ranks of Twitter, Facebook, and Pinterest for giving links more visual love in the stream.
As it turns out, this article talks a little more about what you should be thinking about when it comes to social media posting, and I can't help but smile at what this is going to do for my results :D
UPDATE: These link shares are now all nofollow.
(More info on the new look for links from : http://www.googleplusdaily.com/2014/03/google-link-posts-receive-massive.html )