I have not been using iOS much regularly, so some of the items below may already be possible in iOS 9.x, but are some of the features and flexibility I'd like to see in iOS 10. Some or all of the suggestions below have likely already been surfaced, however, are enhancements I think would make iOS more appealing capable, and flexible.
1. Place and arrange icons wherever I want on the homescreen(s).
2. A native iOS local user space "My Files" or "Documents" just like on OS X, Windows, Android, Linux.
3. Ability to download files from Safari and store them in the native iOS local user space "My Files" or "Documents".
4. Ability to download files from Safari and store them in a cloud storage service like iCloud Drive, Google Drive, OneDrive... - if this feature does not already exist.
5. Ability to drag/drop documents, files, music, etc. from a computer to the native iOS local user space "My Files" or "Documents" just like on Android, BBOS.
6. An "Advanced Settings" mode for those who want more control over the various settings, ability to enable and expose advanced features, or just want to learn more about options available. A feature that can be turned on/off.
7. Ability to choose default apps, say Google Maps as the default over Apple Maps.
8. "Share to/with" capability like that available on Android today.
9. A notification feature that can illuminate the home button similar to the notification lights available on various Android and Blackberry devices. A feature that can be turned on/off. Realize that hardwear capability at the home button level must exist.
10. Support for iOS level Apple Pencil integration and capabilities with the native iOS apps (3rd party even better) just like on the Note 5. If the iPhone 7 Plus had a physical slot to hold an Apple Pencil (sized for the phone form factor) that would be even better. Realize that hardware capability/form factor must exist.