There's a new message on the experimental homepage that welcomes users to the new YouTube and explains one of the new features: "What to watch shows you new activity from your subscriptions, recommendations based on videos you've watched and your taste in videos, plus the most popular videos on YouTube". YouTube also links to a page that was used the last time when YouTube was redesigned. You can see the old page in Google's cache, but now the page returns a 404 error message.
YouTube has constantly tested new versions of the sidebar from video pages. This time there's a new sidebar section that shows other related videos. You can "get the search results, feeds, and channel videos you were just looking at". For example, you can perform a search, click one of the results and see the list of results by clicking "more results" in the sidebar, instead of going back to the search results page.
The sidebar is the most important thing about the new YouTube interface because it's always there: on the homepage, the settings page, the search results page and can be expanded when you watch videos.
To try the new YouTube interface, check the instructions from this post.