Should I accept pingbacks?

I am posting backlinks to blog posts via other pages and then I get a notification of a pingback. First off does this mean that the backlink has been indexed or something by Google?

Secondly, do I need to approve the pingback for it to constitute as a backlink? I did for one and it appeared in the comment section of my blog, which i didn’t want because it was just a snippet of the content that I had posted on an article directory.

What are your thoughts?

Thank you for your help.