JRouter is an abstract class to create and parse routes. You need to write your own concrete router Class to make use of its functionality. The Joomla CMS uses the JRouterSite class as concrete router implementation. For further information see below.

JRouter, the Joomla CMS and writing your own SEO components

JRouter is an abstract class of the Joomla Framework. The Joomla CMS is a concrete application, using the Joomla Framework. Thus, they have created their own concrete Router class, which handles routes. This concrete Router is called JRouterSite and can be found in includes/router.php.

If you take a look at the private _buildSefRoute method of this class, you'll quickly realise that the Joomla Developers allow you to create your own custom routing handlers for each of your components. This way you can make your components SEO friendly. If you want to learn how to write such an handler, take a look Supporting SEF URLs in your component and visit the section The Component Router