1. From the Oxford English Dictionary:
Etymology: < Latin barbar-us, < Greek βάρβαρος + -ous suffix: preceded in use by the simple barbar n., without suffix. The Greek word had probably a primary reference to speech, and is compared with Latin balbus stammering. The sense-development in ancient times was (with the Greeks) ‘foreign, non-Hellenic,’ later ‘outlandish, rude, brutal’; (with the Romans) ‘not Latin nor Greek,’ then ‘pertaining to those outside the Roman empire’; hence ‘uncivilized, uncultured,’ and later ‘non-Christian,’ whence ‘Saracen, heathen’; and generally ‘savage, rude, savagely cruel, inhuman.’ The later uses occur first in English, the Latin and Greek senses appearing only in translators or historians.
2. From the remarkably erudite website Laudator Temporus Acti, an entry on the etymology of barbarian:
Wednesday, September 08, 2004
Barbarians and Beards
Barba means “beard” in Latin, and when the Romans called hirsute foreigners barbarians they were strictly calling them “bearded men,” though the word shortly came to mean, rightly or wrongly, “rude, uncivilized people.” A barber was, of course, one who cut beards or hair. The barber pole outside barber shops today has its origins in the ancient barber’s duties as a surgeon and dentist as well as a hair cutter. It was first the symbol of these professions — a blood-smeared white rag. However, barbarian may have Greek origins.
This is misleading and incorrect. The derivation of barbarian from Latin barba is totally bogus, a folk etymology. The word barbarian is indubitably (not just possibly) Greek in origin, preceding even Homer (cf. barbarophonos at Iliad 2.867). Anyone who didn’t speak Greek sounded like they were saying bar-bar, and by definition any non-Greek was a barbarian.