(You): What ipad app lets me see and manipulate the ipad’s hard drive directory structure/etc?
(Steven): None. It cannot be done.
(Joseph): Neither Cydia, nor the App Store has such a utility; You need to jailbreak your iPad, and you can alter the directory from your computer (Finder, Windows Explorer, etc.) like you would on any removable media.
[Vark assigned category: hard drive, more details]