This is using the old style of file uploads (PHP3 compatible), which requires register_globals to be turned ON. $statfile_name is one of the variables generated by php when a file is uploaded using a file input named 'statfile'. It refers to the original filename. The newer way, for servers with register_globals turned off, is to use the $_FILES superglobal. So, for the same thing, you would use:
$filename = $_FILES['statfile']['name'];
Refer to Handling File Uploads in the PHP manual, they do a great explanation of it 🙂