[php] Clear the form field after successful submission of php form

They remain in the fields because you are explicitly telling PHP to fill the form with the submitted data.

<input name="firstname" type="text" placeholder="First Name" required="required" 
value="<?php echo $_POST['firstname'];?>">
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ HERE

Just remove this, or if you want a condition to not do so make a if statement to that echo or just cleanup the $_POST fields.

$_POST = array(); // lets pretend nothing was posted

Or, if successful, redirect the user to another page:

header("Location: success.html");
exit; // Location header is set, pointless to send HTML, stop the script

Which by the way is the prefered method. If you keep the user in a page that was reached through a POST method, if he refreshes the page the form will be submitted again.