To be clear, you could already use Dropbox with Windows 10 -- the standard utility that keeps a particular folder and its files in sync across all your devices already existed. Dropbox is targeting this new app towards tablet users who might not necessarily keep every single file in their Dropbox synced to their device.
By default, the app gives you a look at everything stored in your Dropbox, regardless of whether or not it's actually stored locally on your Windows 10 device or not. In that way, it's not dissimilar to the Dropbox apps for iOS and Android. What is notable here is how well the Universal Dropbox app integrates with the Windows 10 explorer -- you can drag and drop files from Explorer into this app to save them to your cloud storage.
If you're not running the app, you can still get interactive notifications when someone shares a folder with you; you can click the notification to accept the invite. Right-clicking the Dropbox taskbar icon automatically brings up a list of your most recent files. And you can use the "Windows Hello" face, fingerprint and iris detection features to unlock your Dropbox.
There's also a "quick search" feature in the app -- just start typing and Dropbox will show you files related to your query. And lastly, Dropbox is bringing some a feature that typically live only in its web view to Windows 10: you can add comments to your files and @ mention a shared user to bring their attention to something you're working on together.
While this app can run on any WIndows 10 device, be it a traditional desktop or a tablet, it seems like it'll make sense to run it on a device that doesn't already have the standard sync utility installed. Indeed, it's a bit confusing that there are now two apps you can use to manage your Dropbox for Windows, which probably explains why Dropbox is targeting this release to tablet users.
The company also says that this new app will be updated to support Windows 10 smartphones in early 2016; it will essentially support the same features as you'll find in Dropbox's iOS and Android apps. That's good news, though not a big surprise given how closely Microsoft and Dropbox have been working lately.
Update: This post originally said that Dropbox would have three apps for the Windows 10 platform when it launches its Windows 10 moblie app later this year. It'll actually just have two: the sync client and the new app detailed in this article. That new app will receive an update so that it supports Windows 10 mobile as well as the full desktop version.