What process gives a user access to a file system on a mobile device with full permissions, essentially allowing the user to do anything on the device?

Answer: jailbreaking

Explanation:

Jailbreaking is the process by which Apple users can remove software restrictions imposed on iOS and Apple products like the iPad, iPhone, iPod, and more. Jailbreaking allows root access to iOS. It lets users install applications, extensions, and other software applications that are not authorized by Apple's App Store.