iCloud Drive brings new functionality to iCloud for those running iOS 8 and OS X Yosemite. Even Windows 7 and later can join in the fun via iCloud for Windows 4.0. While iCloud Drive adds the ability to use Apple's massive data centers for general storage, there are limitations when using iOS 8.
Spoiler alert: there is no Finder equivalent or iCloud Drive app for iOS that provides browse access to all of the files stored in an iCloud account. Individual apps such as the iWork suite are iCloud Drive compatible, and will only provide access to files associated with the app.
Many third party iOS apps can utilize iCloud Drive, however to view everything stored in an account the Finder in Yosemite or a compatible web browser must be utilized. In order to browse iCloud Drive files, the service must be properly configured.
Once the iOS device is updated to iOS 8, the one-way upgrade to iCloud Drive can be accomplished from Settings -> iCloud -> iCloud Drive -> Upgrade to iCloud Drive. To see what files are stored in iCloud Drive from a Mac running Yosemite, navigate to the Apple menu -> System Preferences -> iCloud and sign in with the correct Apple ID. Files will appear in the Finder under iCloud Drive, listed in the sidebar.
It’s possible as the service matures that Apple or a third party developer will offer an iOS app to browse and manipulate files on the iCloud Drive. In the meantime, full access to the contents of the cloud service will only be visible from a computer.