There's not much new in the redesigned Surface app from the Windows Store. The app has been revamped to offer a uniform, Windows 10-friendly experience. But, this version is also intended to fix a glaring issue where the Surface Pro 3 pen stopped working after the Windows 10 upgrade.
If you're a Surface Pro 3 user, you may have become accustomed to using the click-to-open OneNote feature of the Surface pen. After your upgrade to Windows 10, you may be one of many who experienced this feature to stop working.
This update should fix that problem and many have already reported that it has. So, you get a fix and UI redesign in one update.
The update should happen automatically, but if you don't have the app yet, you can snag it here: Surface App
Sift through the images above for a glance at the new UI.