Trackback helps you to notify another author that you wrote something related to what he had written on his blog, even if you don’t have an explicit link to his article. This improves the chances of the other author sitting up and noticing that you gave him credit for something, or that you improved upon something he wrote, or something similar. With pingback and trackback, blogs are interconnected. Think of them as the equivalents of acknowledgements and references at the end of an academic paper, or a chapter in a textbook.
Here is a definition from David Maister: Trackbacks are a courteous practice peculiar to the blog world that makes a conversational link between blogs, similar to comments. When bloggers link to another blog, they can send that blog an alert saying, “Look! I’m talking about your ideas and linking to your site.” The blogger who receives the trackback can publish it on his or her site so readers can follow a conversation as it moves from one blog to another.