Following example illustrate filling state (province) drop-down on basis of country.

Drop-down HTML

<select id="countryDropBox">
   <option value="">--Select Country--</option>
   <option value="1">India</option>
   <option value="2">Italy</option>
   <option value="3">Newzealand</option>
</select>

<select id="stateDropBox">
    <option value="">--Select State--</option>
</select>

Example of ajax call via jquery

<script>
    $(document).ready(function(){
        $('#countryDropBox').change(function(){
            var countryId = $(this).val();

            $.ajax({
                  type: "POST",
                  dataType: "json",
                  url: 'ajax&#95;getState.php',
                  data:'cid='+countryId,
                  success: function(data){
                       $.each(data, function( key, val ) {
                           $('#stateDropBox').append("<option value='" + key + "'>" + val + "</option>");
                     });
                 }
            });
        });

    });
</script>

here, we intent to receive json of related states (provinces) from stateDropBox.php file, which would have something like

$cid      = $_POST['cid'];
$core     = Core::getInstance();
$query    = 'SELECT * FROM terms WHERE country_id = :cid';

$pdoObject = $core->dbh->prepare($query);
$queryArray = array(':cid'=>$cid);
$pdoObject->execute($queryArray);
$pdoObject->setFetchMode(PDO::FETCH_ASSOC);

$result = array();
while($row = $pdoObject->fetch()) {
    $sid = $row['state_id'];
    $result[$name] = $row['stateName'];
}

echo json_encode($result);