Open Graph is a standard set of tags that are added to the head section of an web page. It provides meta information, such as author, title, image, and so on. It is mainly used by the social sites Facebook, Twitter, and Pinterest. When someone shares a link the social site gets information to show from the Open Graph data. It is considered a best practice to include Open Graph data, and most SEO plugins will add this to your pages for you automatically.
Open Graph is explained in more detail in this post from the Slim SEO team.