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That piece of code is specifically to display child elements of a certain page. The first line could be called the selector, as you can see it is only grabbing pages which have the parent set to $a.

If you are just feeding the current page slug into $a it will not work on a subpage, this is because there are no pages that have the subpage as parent. If you want to use this code snippet you’ll want to make some sort of check like:

• If this page has no parent, put this page’s slug in $a.
  
• If this page has a parent, put this page’s parent’s slug in $a.
  

I hope you get the gist of it.