For a partial page refresh, you can use JavaScript / Ajax, for example with a Framework like jQuery. There are many examples on the web for dynamic page updates with Ajax.
The Ajax call submits the request to the HTTP server as a HTTP GET or POST request. The code in IdHTTPServerCommandGet checks if the request matches the URL and HTTP method, and then builds and returns partial HTML code.
On the client side, the JavaScript code places the received partial HTML in the specified document tree location.
See for example:
https://stackoverflow.com/a/3644604/80901
Update: a jQuery Ajax based demo can be found at http://www.habariwebcomponents.de/demo/ajaxstats.html with Delphi source (based on my HTTP service library for Delphi and Free Pascal)