Rooted, or rooting, is a rather new term primarily for Linux-based smart phones.
In every version of unix, linux, SunOS, AIX, HPUX, etc, there are several user id's that are set up by default. Some of them run things, others are mostly just a holding and controlling place. The root id, has a UID (userid) of zero. It is all powerful. If you have the password to the root id, you can use it. I've honestly not read how they're getting into the various phones, there could be some other things "wrapped" on top of root to hide it, or the normal ways to hack into it, nevertheless, this is the goal, to get full access to the root id.
What does this do? If you're not a coder or sysadmin, this may seem like not much, but it is everything due to the way the operating system manages permissions. In a nutshell, root has, or can assign to itself, permission to all files and directories, and all users. EVERYTHING in unix/linux can be treated as a file to an extent, so if you have access to every file, you have access to every possible function now or added in the future, as long as it is part of the Linux operating system that root controls. There can be some things that are hardcoded into electronics/chips on the phone that are not under Linux, and therefore root, control. But anything you think of as a program or application is, and some that you may not realize are programs are.
So with root, you can add, own, edit, delete, ANY file on the system, and control who else (what other user id's) have access to what files (programs, apps, functions). Again, think - all powerful.
Hope this helps more for the layman.
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