After editing a file using Box Edit, simply save your changes in the native application. All changes will be saved back to Box automatically as a new version of the file. You will see a status display stating, <Filename> has been successfully saved to Box.
Note: When you save your file, be sure you hit Save in the native application and not Save As. If you select Save As, you will be creating a new copy of your file on your machine, and your changes will not be saved back to Box.