Rodriquez has provided a few simple steps to place folders within folders:
Drag one app onto other app and, as soon as the animation for creating a folder starts, tap and drag any folder you want into the new opened folder. If you’re quick enough, the chosen folder will go into the new folder.
The best thing about this workaround is that it works on stock iOS devices, meaning that no jailbreak is required. Nested folders allow for you to better organize your Home screen with a basic filesystem of sorts. Just like Apple decided to finally allow Newsstand to be placed in a folder, hopefully the company will eventually allow for users to place folders within folders by default. For now, this trick will suffice.