Try this:
<?php /* the php */ ?>
<?php
if ($_POST['submit']) {
// must work
echo $_POST['contact_list'];
};
?>
<?php /* and the html */ ?>
<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>teszt</title>
</head>
<body>
<form method="post" action="<?php echo $_SERVER['PHP_SELF'] ?>">
<textarea id="contact_list" name="contact_list"></textarea>
<input type="submit" name="submit" value="Send" id="submit"/>
</form>
</body>
</html>