Root or Superuser is the name of a user profile with administrative rights on android devices.
Some Apps need Superuser access to work properly. (But be aware that rights come with risks, such as deleting important system files.)
Some other Apps won’t work with a rooted phone. You can hide root with RootCloak.
The Fairphone 1 is a rooted device, which means that the user has more rights to tweak and personalize the appearance and functions of the phone.