Apple's Worldwide Developers Conference gets underway in just a few hours, but it's never too late for leaks! iOS developer Steve Troughton-Smith has discovered an App Store entry for an Apple-published app called "Files." The listing appears to be a stub used to re-enable pre-installed first-party applications that you choose to delete, something Apple added support for last year in iOS 10.
There's not a whole lot of information up right now, but the name of the app and its icon strongly suggest that Apple plans to add some kind of local file manager to iOS 11. There are dummy screenshots listed for both iPhone and iPad versions of the app, so it shouldn't be an iPad-only feature.
The Files app will presumably be more or less similar to the iCloud Drive app Apple added to iOS 9—it would just offer access to local apps and files instead of those stored in Apple's cloud. The app will also presumably stop short of exposing iOS' filesystem to the extent that the macOS filesystem is exposed; even so, an iOS file manager is a longstanding request of many power users, and any app that provides this kind of functionality is a welcome development.
UPDATE: Apple announced the new file manager today. A demo showed that the application will provide access to local files and files in cloud storage services such as Dropbox, iCloud Drive, and Box. It will support nested folders, favorites, search, tags, and a list view in which files can be sorted by size and date.
You'll also be able to drag and drop with other applications, for example by dragging an attachment from e-mail into the file manager. The new manager will be part of iOS 11, shipping this fall.