So, basically it about banning private, not public censorship?
No - it has absolutely nothing to do with censorship. Net neutrality has to do with how internet traffic is handled, though that's a bit of a simplification. Right now all internet traffic is considered equal, so the net is 'neutral'. If this was changed and certain types of traffic or traffic coming from certain addresses were made to be considered a higher priority and thusly would go through faster then the net wouldn't be neutral.
Right now packets enqueue in routers as they arrive, going by a first in first out rules. If non-neutrality was allowed, routers could be set to allow packets from certain locations to skip ahead in the queue and go out faster.