What is a Trackback?
Mell (of Divergent Poles) was trying to understand what a trackback is, so I'm making this post as an illustration.
While creating this message there was an empty spot (just like there is a place for the title) to add trackbacks, since I'm referencing this post (i.e. I'm talking about Mell) I'm adding his trackback information to that spot. When I post this message it'll send a tiny message (called a trackback or sometimes referred to as a ping) to Mell's message and now he'll know I was talking about his post and get a better understanding of this (I hope). There is no indication on my site that I trackbacked him (other than me telling you), the main reason is to let him (and his readers) know I are talking about him and when others read his site they'll know I'm talking about Mell so they might follow the link to see what I say (in this case, if they want to know what I think a trackback is).
Trackbacks are generally for when you are specifically referencing someone's specific message. Sometimes if you're making a similar post or have more information. But I think internet etiquette is it's if you're referencing their specific post. Since I am talking about his post, this is a valid example... I can't even tell you how long it took me to understand this, hopefully my example will make some sense.
The trackback is not just the address for the site or the message, sometimes it's something odd (for this example it's http://haloscan.com/tb/mditangco/110399998884597771) but you don't care 'cause you're just going to cut and paste this part. If you look at his message you'll see it now says “Trackback (1)” (or more, it was 0 before I posted) if you click there it will reveal the first few sentences of this message and the title is clickable and takes you back to this message (which is much more helpful as a link if you started at Mell's and not here), it'll also list any other trackbacks that may have occurred since then.
I use Movable Type and it supports Trackbacks, some software does not, so your mileage may vary.
This is where it gets confusing (the differences/similarities between trackbacks and pings) - Every time I post a post my blog automatically pings a few different addresses so other pages know I updated my page. Why? (I'm glad you asked) Here's three examples. 1) This is so that things like the MovableType home page knows I recently updated and lists me as a recently updated page. 2) And so Blogrolling (see the list of blogs I read on the lower right) know I was updated. On my page if a page has been updated in the last 48 hours and blogrolling knows about it (from a direct ping at http://rpc.blogrolling.com/pinger/ or from looking at some other pingable places) it marks those pages in bold/italics for me and I don't have to do a thing. 3) This same auto-ping alerts Yahoo! so that when (if?) people have me show up on their MyYahoo! start page it knows to update the content for them. This is probably technically called pinging a site but it's probably not that much different than the trackback concept (if not identical). Bottom line, if I changed all the spots on my site to say “pings” instead of “trackbacks” it'd be the same thing.