Joomla Redirect manager component is a new feature which has been introduced in the new version of Joomla 1.7 . It can help you in Joomla SEO or Search Engine Optimization .You can redirect your old invalid URLs to valid or working ones. Without a redirection you will get a 404 error or component not found which is bad for your ranking on search engines.
It is very simple . You can just add the new redirection and make it active. Be sure that you mention the full url to which you are redirecting.
For other details you may visit this .https://docs.joomla.org/Help17:Components_Redirect_Manager