The YouTube app for Android just underwent a major overhaul. It now has a new interface, and it comes with the ability to watch videos in a small window while still browsing YouTube.
YouTube now uses the card-based interface we've come to know from Google's other apps, and it's added the ability to search for and watch playlists. Undoubtedly, the coolest feature is the ability to watch a video in the corner of your screen while you browse YouTube channels. All you need to do is swipe the video down to turn it into a thumbnail, after which you can tap it again to make it full screen again (or swipe it to dismiss it).
The app is rolling out now, and will come to your device between now and tomorrow. If you're impatient, you can grab the leaked APK over at Android Police.