in your PC computer... you know what the ROOT directory is?
it is the main director of all on your harddrive. From the root directory you have full view and access to all other directories.
now, imagine if i locked you into a sub-directory like say the "Desktop" directory. You can only see what is that directory and the sub-directories located in it.
you could never be able to get to the "Windows" or "systems" directory. that would stop you from making any big changes.
Carriers.. are locking you out of the ROOT directory.. keeping you from making any system or OS changes. They think this will be safer for you and the phone. Which in some cases it is!
so.. when you ROOT your android phone... you are giving yourself full access to the ROOT directory. Which means full access!