This was written by a guest writer Peter of KrooClub

This is a diagrammatic representation of Linkbacks. The system of Trackback illustrated here was developed by SixApart, creators of theMovableType blog package.

Its purpose being:

Person A writes something on their blog.
Person B wants to comment on Person A's blog, but wants their own readers to see what they had to say, and be able to comment on their own blog
Person B posts on their own blog and sends a trackback to Person A's blog
Person A's blog receives the trackback, and displays it as a comment to the original post. This comment contains a link to Person B's post 
 
 Now the process has expanded and there are now more than one Trackback definition and systems. Unfortunately the community believes that this model is the current and valid system. Why has it changed?

Since 1995 many blog platforms have been developed and not necessarily directly compatible with each other. Newer systems are security conscious and very few allow direct input into a post by the non-owner. This includes electronic notifications such as some of these linkback operations. Another good reason why this has lost the original plan was because of the abuse by spamming blogs. It was literally a click of a button by another writer to paste their pingback on the original blog which may have had quite a good SEO strength. The electronic ping may have been irrelevant in content to the post but the fact that their URL was published meant that it would be recognised by SEO bots. This was an abuse and an annoyance and stopped a lot of bloggers enabling this facility on their blog.

A current model of a Trackback.
C:\Documents and Settings\Peter C\Desktop\linkbacks\trackback.gif

The model discussed here is an indirect process. It's the process used by Yola through Disqus.

Each blog post has a unique URL called a PERMALINK.  This is a very important aspect and as users we rely heavily on the fact that our blog hosting service will properly index and keep our post indefinitely. It becomes more important for primary reference articles and there's a lot of trust placed in our blog host.

C:\Documents and Settings\Peter C\Desktop\linkbacks\linkback.gif

As mentioned very few blog platforms allow direct access to the post from the non-owner and Yola fits this model. Disqus has been deployed with Yola to manage blog comments. Disqus creates its own PERMALINK and this is associated with the blog post. Disqus provides a Trackback for each post. The Disqus trackback is simply a URL. It is static and has no electronic function as the model displayed above. The URL of the Trackback can be copied and pasted into a new document whether it is a blog post or a flow-on comment somewhere. This allows readers to reference the original post and it also creates a link to the original post. It doesn't appear on the original posters site automatically. Many posters would send an acknowledgment with the Trackback to the original poster and presumably if the original poster was impressed they would acknowledge this and refer to this person's blog. This now becomes a link building exercise and is quite valuable. It really is about establishing relations ships.
C:\Documents and Settings\Peter C\Desktop\linkbacks\pingback.gif

The blog is gaining a lot of new interest as a sales and marketing tool. It's seen as a valuable medium for these processes and is recognised by SEO systems. The model will surely evolve further very quickly.

Currently the Disqus commentary system used with Yola does not include an electronic Pingback. Disqus have developed pingback for some of their clients' platforms so it is likely that it will appear at some stage.

JS-Kit has recently acquired Haloscan, probably the premiere third comment system. They do have a module pingback and I would think that this will become available as part of the option suites in the future. 

The Refback is a semi-automated feature and I haven't seen any reference to its use so I'll leave it as a statement without discussion.

C:\Documents and Settings\Peter C\Desktop\linkbacks\refback.gif
What are the advantages of Trackbacks?

There is the first aspect of recognition and comment. The most functional advantage is the SEO acknowledgment and the viral nature of a subsequent writer using the material and referencing it with the trackback URL. It directs people back to the original blog post and the blog lives on. The numbers game in blogs is important and is becoming more important as marketing targets blogs and sales will follow. The greater the readership the greater the potential number of buyers.

Relationships flourish with acknowledgment and it's likely that the acknowledged writer will also follow the persons who made the acknowledgment. Still the numbers game. Of course there is the authority aspect of a specific blog. A high ranking blog has prestige and SEO power so to be acknowledged and referred to by this higher level can do wonders for the conscientious starter in the field.
 

References:

http://webforumz.com/misc.php?do=linkbacks#trackbacks

http://codex.wordpress.org/Introduction_to_Blogging#Trackbacks