drushd is a library to help you create daemonized drush commands. Why would you ever want to have a drush command as a daemon? Well, think about things like IRC Bots and ongoing tasks like migrations and data cleanup, etc. You probably shouldn't be doing this if you are wanting to daemonize something that has nothing to do with Drupal though. PHP is not the ideal programming language for this sort of thing, but drushd tries to make it better by monitoring memory usage and reforking as necessary.
The best way to get started using this is to look at the example in drushd_example.