the code should probably not say path as in this instance it actually means URL and not absolute path.
your_function like ALL functions you find on these boards go in your CHILD'S functions.php
define('CHILDTHEME', get_bloginfo('stylesheet_directory'));
add_action('wp_head','your_function',1);
function your_function(){
if(!is_admin()){ /* to prevent the loading of your stylesheet in the admin*/
if(is_front_page()){ /* to load a stylesheet for your front page */
wp_enqueue_style('front_style', CHILDTHEME . '/front-style.css');
}else{
wp_enqueue_style('normal_style', CHILDTHEME . '/style.css');
}
}
}
the caps CHILDTHEME is a php constant. i always use constants for the different folders in my theme so that if i ever change the file structure i only need to change the reference in one place. but you aren't obliged to use it.
if you are still confused on the subject please read:
programming.thematic4you.com/2010/01/how-to-use-a-different-layout-for-a-certain-page/
idk if there is a benefit, per se, but doing everything via functions is just sort of the child-theme approach. it keeps everything centralized.