WordPress Child Themes

What are WordPress Child Themes and why are they useful?
http://themehybrid.com/themes/hybrid/child-themes

A case for including child themes in the official WordPress theme directory
http://developdaly.com/wordpress/child-theme-inclusion-in-the-wordpress-directory/

Vote for Child Theme Inclusion in the WordPress Directory
http://wordpress.org/extend/ideas/topic.php?id=3264