There's an update to the Youtube app waiting for you in the Google Play store, and if you're using a 10-inch tablet (like the Nexus 10), you're in for a treat. The update adds a new layout for large screen devices that brings a great two-pane experience to everyone's favorite video service.
The update uses the concept of Android fragments, where both can act independently yet have influence over each other. The smaller fragment on the left allows for things like app navigation and selection, and your content appears to the right. It's a great way to build apps for large screen devices, and allows one app to have the best UI and layout for any size screen.
Hit the link above for the update, or just check your Google Play notifications.