In iOS 9 that totally changed, One of those features is a standalone iCloud Drive app. It’s not immediately apparent, but while launching an app we received a pop-up asking us if we wanted to install it. We were also able to access it via the Settings app iCloud > iCloud Drive > Show on Home Screen.
We’re not exactly sure what all the app is capable of, as it isn’t working for us at the moment, but it appears you’ll be able to access and manage your iCloud documents the way you can with Dropbox and similar services. We’re also seeing iCloud Drive on iCloud.com.