Pingbacks are basically a mechanism to notify blog owners when their post had been referenced from elsewhere.
There’s a good post with example here:
Once approved, your readers will be able to see links to articles where your post is referenced. Additionally, the readers of the blog where the ping back originated will be linked to the original article.
One caveat is the high potential for spam pingbacks. While we do run a spam comment filtering system, it is up to you to approve pingbacks on your site. Do your due diligence before simply approving every pingback to make sure that your article is being referenced from a legitimate blog.