Reason #1: It tells the author of the original article that you're continuing or expanding the discussion on your blog.
Reason #2: When you Trackback, a link to YOUR blog appears on the original author's blog, if they accept your Trackback. Not only are you sending
traffic to the original author, they're sending traffic back to you!
(Notice how many people Trackback to Seth Godin's blog? One reason
people do it is for the traffic.)
Reason #3: You make friends. I've found that to be a successful blogger, you
must become friends with other successful bloggers. One way to quickly
"make friends" is to send Trackbacks.
Then he tells you how to post the trackbacks for yourself.
Image (c) Diane Clancy, Animals IV.