Child theme in WordPress is used to create modifications into the theme. If the parent theme will update than all your modification will not be lost because they were made inside of the child theme.
To create a child theme create new folder inside of the WordPress theme and create file style.css inside of this folder with such code:
/*
Theme Name: Twenty Eleven child theme
Description: Child theme for the Twenty Eleven
Author: you
Template: twentyeleven
*/
@import url("../twentyeleven/style.css");
#title a {
color: #333; /* you can override necessary styles */
}
Activate your theme and enjoy the functionality of the parent theme and the ability to override it.
If you need to override some file, than copy it from parent theme to child theme and make needed modification.