/home/username/www is the same as public_html. Yes, it's a bit confusing, but the www is what is known as a symlink, which is a link that leads to a real directory or file. In this case, the www symlink leads to the public_html directory.
/home/username/tmp contains all your web stats files.
/home/username/mail and /home/username/etc contain mail and it's various configuration files.
/home/username/public_ftp is used if anonymous ftp is enabled
_vti_bin, _vti_conf, _private, etc are all part of Front Page extensions. If you don't see these, don't worry, it just means FP extensions haven't been installed for this account. If you wish to install them, you may do so from your cpanel. (see the section on Front Page Questions to learn how)