Android 4.4 introduces a new interface for accessing files from within apps. Traditionally, trying to upload a file - say, to a social network - created a popup asking which source to pull it from. Now apps will open a sidebar navigation menu that lists all the available options, and Box has already rolled out an update adding support for it.
By default, the new storage access framework only shows local files and Google Drive, but any app that has added support will also appear. This will take no effort on the user's end. If you have the latest version of Box installed, it will appear as an option.
Naturally, you must have Android 4.4 in order to take advantage of this new functionality. Older versions of Android will continue to display Box and other cloud storage options inside a popup.