// HTML ---------------------------
<select id="first">
...
</select>

<select id="second"></select>

<script>
    $('#first').select(function(){
        firstValueSelected = $(this).attr('value');
        $.get('yoursite.com/getSecond',{idFirst: firstValueSelected},function(data){
            $('#second').append(data);
        });
    });
</script>

// PHP -----------------------------

function getSecond(){
    $id = $_GET['idFirst'];

    ///sql and foreach goes here
        $values = "<option>".$row['any']."</option>";
    /// end
    echo $values;
}