A rooted phone is one where the user is in control of the operating system instead of the operating system. You can tell it "too bad" when it tells you that you can't do something like uninstall an app that came with the phone. It also means that you are able to uninstall parts of your OS that make your phone work. Got to be careful.

Greenify is a bully of a program. Normally your OS will leave things running if nothing else needs that memory. Greenify takes those programs and stuffs them into their locker and spins the knob. The operating system doesn't know the combination to open the locker. Only I do. The program can't come out until I say so.

Force stopping an app is making the OS turn it off completely. This doesn't prevent it from possibly restarting.

Freezing the app is making it so that it can't run until it is unfrozen. This is possible with some operating systems without having to root and install something like Greenify.

This is all for Android. Jailbreak is the equivalent for iOS.