One of my readers, Asked:

Hi:
I’m a fellow student of Alex Jeffreys and heard you are the expert on links, etc.
Could you get back to me on the following?

What is a pingback?

Every time I post a new entry, I get one of these ping back comments.

Should I approve them or not?

It seems that my post is repeated on the site the ping comes
from even if I don’t approve the comment. I’d rather not approve them because
I think they clutter up the comment area, but I don’t know if not
approving them diminishes their results.

Thanks, Sandy

A PingBack, just means that someone just talked about your site.

WordPress explains it clearly:

For example, Yvonne writes an interesting article on her Web log. Kathleen reads Yvonne’s article and comments about it, linking back to Yvonne’s original post. Using pingback, Kathleen’s software can automatically notify Yvonne that her post has been linked to, and Yvonne’s software can then include this information on her site.

Most of the time, it’s a spam blog, scraper sites, or RSS scraper.
They post a snippet of your blog post in order to get Fresh content (SEO)
and cheap links from people, building NO Valve what-so-ever.
It’s normally grayhat black-hat blog trick. If’s it one of these type
of comments just delete them!

Sometimes, It’s actually a person talking good things about your blog.
If it is then you might want approve them

It’s fine if you delete the comments, but make sure you check them,
because sometimes it’s a real person.

Does that make sense? – Please Comment if you need further help

-Brad