The term parent directory refers to the link at the top of the page that allows you to navigate "up" one level in the folder structure. If you are looking at a list of specific movie files, clicking "Parent Directory" will take you to the root folder containing all the sorted folders.
: Ensures the page is a standard server index listing. index of parent directory movies better
For those who just want to automate the process, openMovieDL is a Python script that scrapes Google for open directories containing your requested movie, jumps into the directory, and grabs the direct download link. It's designed for "lazy people who can't search all the different websites". The term parent directory refers to the link