This is possible by using AJAX.
The following links are containing more information about AJAX and implementation in WordPress:
Ajax (Asynchronous JavaScript And XML) is a technology that allows a web page to perform actions or update dynamically, without completely reloading
This article, aimed at plugin developers, describes how to add Ajax
When using WordPress as a CMS, situations often arise where you need to display, add or update content on your WP site without turning to plugins. While bolting in some PHP alone can do the job, nothing is more seamless that the magic of jQuery’s AJAX