A WordPress child theme is a theme that inherits the functionality of another theme, called the parent theme, and allows you to modify, or add to, the functionality of that parent theme.
If you want to modify any of the core PHP files, I would suggest looking into child themes so that none of your modifications will be overwritten when you update. If you are using one of my premium themes and only wish to modify some CSS, the Custom CSS editor is the fastest way to go about doing just that.
A while back I create a tutorial on bavotasan.com with instructions on how to create a child theme. Check out Creating a Child Theme in WordPress for easy to follow instructions that will help get your started with your child theme. Also check out the link from the quote above that leads the WordPress Codex page.