Change/remove the text in both places.

To remove, leave the opening and closing single quotes in place. Just remove the text in between.

Code:
  // This section deals with the "home" page at the top level with no options/products selected
  /*Replace this text with the headline you would like for your shop. For example: 'Welcome to My SHOP!'*/
  define('HEADING_TITLE','Congratulations! You have successfully installed your Zen Cart™ E-Commerce Solution.');
} elseif ($category_depth == 'nested') {
  // This section deals with displaying a subcategory
  /*Replace this line with the headline you would like for your shop. For example: 'Welcome to My SHOP!'*/
  define('HEADING_TITLE', 'Congratulations! You have successfully installed your Zen Cart™ E-Commerce Solution.');
}
would become

Code:
  // This section deals with the "home" page at the top level with no options/products selected
  /*Replace this text with the headline you would like for your shop. For example: 'Welcome to My SHOP!'*/
  define('HEADING_TITLE', '');
} elseif ($category_depth == 'nested') {
  // This section deals with displaying a subcategory
  /*Replace this line with the headline you would like for your shop. For example: 'Welcome to My SHOP!'*/
  define('HEADING_TITLE', '');
}