Im not sure if your talking about the trackbacks when you are creating a post, or pingbacks that you get as comments from other blogs, but they are basically the same.
Trackbacks are used to lets other blog owners that you have linked to them. However, if you link to another Wordpress blog this is not necessary. To use a trackback all you have to do is enter the URL of the blog post you are linking too.
You can also enter in the URLs of blog search engines such as http://blogsearch.google.com/ping/RPC2. However, these are hard to find and sites like Pingler.com do a much better job of this. Telling a blog search engine, aka pinging, lets them know you have new content and your site needs to be crawled.
When you get a pingback in your comments that is letting you know that someone is linking to your blog. This comes in handy when other authors decide to scrape your content and use it on their blog. If you have links in your post to other posts you will get a pingback from yourself (kinda redundant but its how the system works). If someone links to your blog, you will get a pingback from their blog post as well as an excerpt of their post. If you click on the link you can see exactly where the link is. If they legitimately linked to you (i.e. didn't copy your stuff) then take it as a complement. If they did steal your stuff you can do one of two things.
You can either comment on the post and ask for them to give you credit for the post and have them add a link to the original post and make all the links dofollow.
Or, you can write them a nasty comment or email saying that they plagiarized your content and if they do not take it down you are willing to take legal action (which does not mean sue).
If they don't respond to either approach then you can tell Google about it (because they are the internet gods) that they have plagiarized your work and probably other peoples work and request that they be removed from the index.
P.S. should I make a Hub about how to use Wordpress? I use it everyday and am quite knowledgeable on how it all works.