In other words, how can I tell if the person using my web application is on the server it resides on? If I remember correctly, PHPMyAdmin does something like this for security reasons.
You can also use $_SERVER['REMOTE_ADDR']
for which IP address of the client requesting is given by the web server.
$whitelist = array(
'127.0.0.1',
'::1'
);
if(!in_array($_SERVER['REMOTE_ADDR'], $whitelist)){
// not valid
}