Passing specific Javascript variable to PHP

It doesn't work the way you suppose. Appending HTML with JQuery doesn't run your server-side PHP script. So it is just a string appended to the wrapper which has no sense from code execution's point of view.

To make what you want to do, you need to use Ajax technology which consists in passing data to server without page reload. So you need to create a server side page which will accept your $id parameter and invoke your delVid function.

// ajaxScript.php (pseudo code)
// I don't know what framework and routing scheme are you using,
// so just a raw code to show an idea

<?php       

function delVid($id) {
    foreach($_SESSION['playlist'] as $key => $value) {
        if($id == $value) {
            unset($_SESSION['playlist'][$key]);
        }
        sort($_SESSION['playlist'], SORT_NUMERIC);
    }
}

delVid($_POST['id']);

Then you need to write JS code which will be perform Ajax request to that page on some event. JQuery has such useful methods as $.ajax, $.get and $.post to implement it.

jQuery(document).ready(function($){ 
  $(document).on("click",".remove", function(){ 
    var vidID = $(this).parent('div').parent('div').attr('id');             
    $(this).parent('div').parent('div').fadeOut();
    $.post('/ajaxScript.php', {id:vidId});
  }); 
});