Getting a variable using $post ajax back from php to js response in WP

You need to send the var through your ajax request:

$.post(
//be suer that this var is pointing to wp-admin/admin-ajax.php
WPaAjax.ajaxurl,
{
    action              : 'my_php_action_to_do',
    //here your var and its value
    my_var              : 'the_value'
},
function( response ) {
    response = jQuery.parseJSON(response);
    alert(response.message);
}
);

In your my_php_action_to_do function:

function my_php_action_to_do(){
    $var['message'] = $_POST['my_var'];
    //Send back the $var value in json format. You can send it in other format if you want
    echo json_encode( $var );
    exit();
}

//Don't forget to add your my_php_action_to_do function to wp_ajax_* action hook.

add_action('wp_ajax_my_php_action_to_do', 'my_php_action_to_do');
//or this if you want it to work in the frontend
add_action('wp_ajax_nopriv_my_php_action_to_do', 'my_php_action_to_do');