The new design puts notifications at the front-and-centre, with them appearing alongside messages and friend requests in the top left corner next to the site's logo. The search box also now sorts according to how close a friend a person is to you - how many friends you have in common, etc. The photo uploader has seen improvements too.
Some things have disappeared. The bar along the bottom is still there, but only just. There's far less content residing in it now - just chat and translations. The news feed has also dropped the "News Feed" and "Live Feed" delineation in favour of "Top news" and "Most recent". That should help clear up any confusion.
Lastly, Mark Zuckerberg has also said that the site will be rolling out "something cool" once a month from now on. He didn't elaborate on exactly what, so we'll just have to wait and see. We're hoping for a pony.