Pings and trackbacks fall in the same category and basically do the following: say you write a very interesting article on your website. I could comment on it, but suppose it is rather lengthy, and I want to post it on my own site instead.
In that case I write an article on my own blog, and “trackback”, so I take the trackback link from your post, put it in the “trackback” field of my own post (in my own “write” page) and:
– my post will appear on my own site as my own post
– my post will appear on your site as a comment to the post
pings are more sophisticated because they use a xml-rpc protocol, but basically do the same.
The beauty of this system has one downside: you can disable comments to avoid spam, but when trackbacking is allowed, comments (and comment spam) can still come through from unregistered users.