If you wish to display some content that only those facebook users can see who liked your page, then you need to write this little piece of code to verify:
$signed_request = $_REQUEST["signed_request"];
list($encoded_sig, $payload) = explode('.', $signed_request, 2);
$data = json_decode(base64_decode(strtr($payload, '-_', '+/')), true);
if (empty($data["page"]["liked"])) {
//do if user has liked your page
}else{
//do if user has not liked your page
}
This technique is good, if you want to have more likes on your facebook pages.