The window that comes up is your space on MobileMe. You get 20 GB normally and you can add space if you need it. Unless you change the distribution, 10GB are for Mail and 10GB are for iDisk. You can put any files you want into these folders. The Public folder allows you to share files with ANYONE. They can see the files at http://public.me.com/username (username being your user name).
Like any file on your Mac, all you need to do to share the file, is drag and drop it onto the folder you want. Then, from any other computer you can access this folder and retrieve the file.
QED