public_html is where you upload your web files. Anything you place in this folder will be viewable on the web.
www is the same as public_html. It is there for compatibility reasons. www is linked to public_html(symlink).
tmp contains all your stat logs for Awstats.
mail and etc contain mail and it's various configuration files.
public_ftp is used if anonymous ftp is enabled. This is disabled by default.
_vti_bin, _vti_conf, _private, etc are all part of Microsoft Front Page extensions. If you don't see these, this means FP extensions haven't been installed for your account. If you wish to install them, you may do so from cPanel.