it means that you modify the phone in order to obtain read/write access to the root directory, or / in Android/Linux terminology.
the attached screenshot shows what the root directory looks like. if you can obtain "superuser" access to all of the files contained therein you can essentially do what you want with your phone.
eh. remove all unwanted apps and the associated file repositories. for whatever reasons, Google and the phone manufacturers don't want you to delete the junk they ship with the phone.
for cheaper phones this means the precious storage space is taken up by garbage that discerning users neither need nor want.
rooting a phone is a term that describes various methods of circumventing the security measures that Google and the phone manufacturers put in place to stop you messing around with the system files.
in theory this restriction is a good idea because it safeguards the user against malicious apps etc. or just messing around with the system configuration files and bricking the device.
in practice it's a right royal PITA because you can't get rid of the dozens of unnecessary apps that they load the phone with. you also can't add a whole bunch of really cool third-party features that the dev community comes up with. their creativity knows no bounds, unlike the shortsighted Google and their telco lapdogs ????