Naffed off means: British slang meaning annoyed or irritated - the past participle form of 'naff off' used as an adjective for the state of being fed up or put out. 'Naffed off' is slightly softer than 'pissed off'. It is informal slang, fine in casual speech but not suited to formal contexts. There is no real cause for parental concern; it is descriptive vocabulary rather than risky behaviour.