Just to add on to what Media Girl said a bit:

“Permalinks” are human-readable. They’re the links you use to get to a post in your web browser, even if the post has fallen off the front page of the blog. (Hence “Perma[nent] link”.)

The “TrackBack” URI is an address for a machine-readable conversation where one blog tells another that it referenced a particular post. (If you try going to a “TrackBack” URI in your web browser, you’ll most likely get an error message in XML.) Since the TrackBack URI doesn’t convey any useful human-readable information, ideally blogging software should be able to embed this information in a page where humans won’t see it, and should be able to extract it automatically from pages that you are sending TrackBack pings to. But in this vale of tears that very often doesn’t happen, so most blogging software displays a TrackBack URI somewhere for manual cut-and-paste. Yet one more way, I guess, in which technological gizmos make our world a little more useful and a little more ugly.

HTH.