How to hide breadcumbs on the front page?
Assuming you are using D7.  There are a number ways to achieve it. I am providing three methods here. 

Contributed module. 
The easiest one is to use "Disable Breadcrumbs" module. 

Theme Overide. 
If you think it is overkill, don't want to use that module, you can also implement the preprocess html hook to remove breadcrumb like this:

/**
 * Implements template_preprocess_html()
 */
function THEMENAME_preprocess_html(&amp;$variables) {
  if ($variables['is_front']) {
    // kill breadcrumb, set to empty array
    drupal_set_breadcrumb(array());
  }
}


Custom Module. You can also done this in your custom module by implementing hook_page_alter

/**
 * Implements hook_page_alter().
 */
function MODULENAME_page_alter(&amp;$page) {
  if (in_array('front', $page['#theme_wrappers'])) {
    // kill breadcrumb, set to empty array
    drupal_set_breadcrumb(array());
  }
}