Nested folders (or, folders within folders) are one of the most useful features of iOS 7. Unfortunately, it's more of a glitch than anything Apple intended to include, so there's no official guide from Apple on how to do it. But don't worry; we're here to help.
Placing folders within folders is a fantastic way to clean up your home screen, and it can be a godsend if you want to send unwanted, undeletable apps into a dark, unseen corner.
Here's how to pull it off:
We'll start with these four apps, but you can use absolutely whatever apps you want.
1. First, we combine two apps to create a folder, and then combine the remaining two apps to create a second folder.
2. Now, hold a finger on one of the folders so that it becomes grayed out.
3. As soon as it does this, press the Home button twice to bring up the multitasking menu. This trick will not work if the apps begin to wiggle (when they enter the organization mode) before you hit the home button. You have about a half a second to get this right.
4. From the multitasking menu, click on the home screen. You should see the folder icon remains enlarged and grayed out, and also that the folders are now wiggling.
5. Now, click the destination folder (the one you want to add the first folder to). You should see the icon of the first folder hovering above.
6. Now, click the home button once. Ta-da! You now have a folder within a folder. The best part is that these folders work flawlessly, and you can navigate through them, launch apps from within them and remove apps just as you would otherwise.
You can use this trick to further nest additional folders, and I've been able to create five folder levels before eventually stopping, though I'm pretty sure you can just keep going until you get bored.
This glitch was first noticed during the iOS 7 beta, and though I'm sure Apple is aware of it, they haven't taken any steps to correct it, and as of the current iOS 7.0.1, it still works perfectly. In fact, during the beta phase, any nested folders you had created would reset to the home screen after a device restart, but that's been changed, leaving all nested folders in place when the phone is power cycled.
That said, the company could squash this at any time, so if you really fall in love with nested folders (as I have) take care before updating.
Update: How to add apps to already nested folders
You can add apps to already nested folders very simply, though it's slightly more complicated than just dragging the app to the folder.
First, highlight the app you wish to move by holding your finger on it and then immediately double-tapping the home button, just as you did in Step 3 above. Now, from the multitasking menu, click on the home screen.
Then, click on the first folder (the one holding the nested folder you want to move the app to), and then click on the nested folder. Once inside the nested folder, click the home button once and the app will relocate itself. Easy!