Here are the instructions to put a folder inside a folder, via AppAdvice:
First, tap and hold on a folder, then immediately double press the home button. Now, tap on the home screen card within the multitask switcher. The folder should now look similar to the over-sized folder below. Next, open another folder and press the home button and the first folder will follow you into the second folder. I haven’t found a limit to this nested folder glitch, but I’ve only nested about six folders so far.
A restart brings back the folders to their original state.
Although this seems to be a glitch, it’s important to note that hidden settings in iOS 7 does indicate that Apple may allow us to create nested folders in the future. If this is indeed a bug, though, it’s likely Apple fixes this in the next beta version of iOS 7, which is rumored to be released on the 8th of July.