Permalinks are very simply the URLs that point to specific blog entries on a website.  Usually, when you click on a permalink, you can access other functions and information such as commenting and "intrasite links" (my invention).  Most permalinks have some sort of date structure like "/2006/08/28/nice-wordpress-title/" or "/2006/08/28/ugly_movabletype_title_.html" (mentioned here).  Other permalinks just have a sequential numbering system like "?p=1233" or "/archives/005694.html". 

I'm really not a fan of numbered permalinks because they don't say anything about what they're linking to.  Mental Floss links to other articles on its site quite a bit.  But if you mouse-over the link, you don't learn anything new about where the link will send you.  Boing Boing, on the other hand, uses date-based permalinks.  You can usually get a pretty good idea of where each link will send you, and you also know when the respective articles/posts were written. 

However, I can also see the benefit of having sequential permalinks.  I can even see the benefit of having title-less posts.  Instead of writing concise, organized posts about fairly specific topics (I've pretty much mastered the art of describing a post in 2 words or less), you can write about anything you want with no boundaries or restrictions.  There's no such thing as a side note or an unrelated thought.  It's all freeform and stream of consciousness (sorta).  Personally, I think it's a good idea to have organized thoughts in one location and unorganized thoughts in another.  At times, it's nice to have a structured archive of previous thoughts and opinions.  Other times, it's good to just vent.