Pingback lets you notify the author of an article if you link to his article (article on a blog, of course). If the links you include in an article you write on a blog lead to a blog which is pingback-enabled, then the author of that blog gets a notification in the form of a pingback that you linked to his article.

If you're feeling really geeky you may want to check out the Pingback technical specification or Otto's "How Pingbacks Work" explanation.