You need to do that on the client side for instance with jQuery.
Let's say you want to retrieve HTML into div with ID mydiv:
<h1>My page</h1>
<div id="mydiv">
<h2>This div is updated</h2>
</div>
You can update this part of the page with jQuery as follows:
$.get('/api/mydiv', function(data) {
$('#mydiv').html(data);
});
In the server-side you need to implement handler for requests coming to /api/mydiv and return the fragment of HTML that goes inside mydiv.
See this Fiddle I made for you for a fun example using jQuery get with JSON response data: http://jsfiddle.net/t35F9/1/