In a nutshell, TrackBack was designed to provide a method of notification between websites: it is a method of person A saying to person B, “This is something you may be interested in.” To do that, person A sends a TrackBack ping to person B. TrackBacks are typically sent from one blog to another when one publishes a post that includes a link to the other blog.
The idea of a TrackBack is based on the principle of push, rather than pull. If you want to share information with another website, you initiate the connection, rather than waiting for the other website to discover you (and your information).
Sending a TrackBack is often called a TrackBack ping. A ping in this context means a small message sent from one webserver to another.
See the article on sending a TrackBack for more information on how to send and receive a ping.
Uses for TrackBack
Currently, the main use of TrackBack is as a remote commenting system: if I post on my blog about a post on your blog, my blogging tool will notify yours to inform you of that. Your blog will then display the excerpt of the post that I made, with a link back to the post on my site. This allows visitors to your site (and you) to know what others are saying about your post--like comments, in other words, but the post is on my site instead of yours, as it would be if I had just left a comment. Unlike comments, I will still be able to edit my post. In other words, TrackBack provides more control over your content.
The power of this method is that the TrackBack ping has created an explicit reference between my site and yours. These references can be utilized to build a diagram of the distributed conversation.
Although TrackBack's most prevalent use thus far has been as a form of remote commenting, a more exciting use has been emerging: using TrackBack to aggregate content into topic-based repositories. This was actually the original intended use of TrackBack--the remote commenting grew out of a special case of a topic-based repository, the "topic" being a single blog post. Content aggregation sites collect content about a particular topic.
A more detailed description of TrackBacks and more resources about them can be found at Wikipedia.
TrackBack was first released as an open specification in August 2002. It was released as both a protocol and as a feature of Movable Type 2.2, which contained the first implementation of TrackBack. Since the true value of TrackBack only comes when many sites support it, TrackBack was always planned as an open system: a system that could be easily implemented in other blogging tools.