What is a "pingback" (see details)

I have been writing a blog and recently used a free article from Articles Base to illustrate a point more on a topic I was discussing. I left the original authors information intact and a link back to the original article.

This morning I had a comment to moderate and it said that it was a pingback.

Apparently another site had picked up the article off my blog and wants to pingback to my site as the source. I looked at the article and they left off my commentary and it is only the article from articlebase.

What is common protocol on this? What is the function of this pinging? I am able to edit this ping- should I edit it back to articles base and publish or should I reject the ping. If I reject the ping will the world explode?

Many thanks for any input.