How to reload a div without reloading the entire page?

I suppose what I am asking is really easy for most of you. I want to reload a div without reloading the entire page. What's the best way to do it?

<div class="black_text" id="cp_in_content_div">
<?php
$id = $_GET["id"];
$result = mysql_query("SELECT * FROM Setting WHERE ID = $id");
$row = mysql_fetch_array($result);
switch ($_GET["action"])
{
    case "delete":
    if (!unlink("$_SERVER[DOCUMENT_ROOT]setting/$row[Filename]"))
    {
        echo "Error.";
        header("Refresh: 2.5; URL=delete_setting.php?id=$id");
        exit();
    }
    if (!mysql_query("DELETE FROM Setting WHERE ID = $id"))
    {
        echo "Error.";
        header("Refresh: 2.5; URL=delete_setting.php?id=$id");
        exit();
    }
    else
    {
        echo "Ok!";
        header("Refresh: 1.25; URL=index.php");
    }
    break;
    default:
    echo "form";
}
?>
</div>

I need those header("Refresh:...") to only reload the div instead of the page.