Since the Xbox One runs a universal version of Windows 10, it's easier then ever for developers to make apps for the video game console. Thus, we now have a Dropbox app for Xbox One.
So yeah. If you wanted to access your Dropbox files (like pictures or movies) on your Xbox One, you can now do that. I suppose it could be useful for getting slideshows of family pictures or ripped DVDs to play on your Xbox, assuming you use Dropbox to store things like that. The app can also import content from attached USB drives, if importing files to your Dropbox account through your Xbox is something that was missing from your life.
The app can also import screenshots directly from the Xbox to Dropbox, which may be more helpful to some people than using OneDrive. The app is available today on Microsoft's Xbox Store.