Use Ajax for this.
Build a function that will fetch the current page via ajax, but not the whole page, just the div in question from the server. The data will then (again via jQuery) be put inside the same div in question and replace old content with new one.
Relevant function:
e.g.
$('#thisdiv').load(document.URL + ' #thisdiv');
Note, load automatically replaces content. Be sure to include a space before the id selector.