There are now two main menu items in the ftp explorer: "Server" and "File/Folder".
The second one features commands for manipulating with files; now you can cut/copy/paste files across server(s) and rename/delete files you want.
This new feature has been put on
beta.phpanywhere.net for testing. It is in early development stage and needs to be tested.
Also, new features are being developed. You will be able to create files, create/copy/delete folders soon and upload/download files.
In the future you can expect support for copying large files.