Barbarian is a term generally used to refer to "primitive" people who lack "civilization". Nobody ever referred to themselves as a 'barbarian", but instead used the word to refer to others. It has been variously applied to the Goths, the Norse, the Germans, the French, the English, the Welsh, the Irish, the Scots, the Huns, Native Americans, Pagans, Muslims, Hindus, Christians and just about anyone the speaker doesn't like.
The term barbarian comes from the ancient Greek barbaroi, which literally means "those who speak like sheep" (i.e bar-bar!), an unflattering term for non-Greek-speakers. The ancient Greek definition of barbarian, therefore, was "anybody not Greek." This was similarly the origin of the name "Barbary Coast" for North Africa as they spoke a non-European language there.