I notice with the Rocket Theme site that every time I return my name and password are always there in the login box and all I have to do is press the login button. Also when I close the browser and come back to the site I am still logged in.
Is this a plugin or something else as I would like it as a feature on my site
Joomla uses session variables to store your "logged in" status. They're set to expire after a certain time period. You can explore the values of the session variables by dumping the $my, $mainframe and $_SESSION variables to output.
I would guess that the rockettheme site is holding your username and password in cookies, which can be accessed whenever you come back to the site. Cookies also have an expiration date, but that date can simply be set to way off in the future every time somebody visits.