The word Britain dates to the 1300's, and there have been a variety of spellings over time. The Oxford English Dictionary lists breonete as the first attested form of this word in English in 1225. It comes from Latin Britannia with some influence from French Bretaigne. An earlier Latin form was Brittania from Brittani ("the Britons"). Briton comes from Anglo-French Bretun, which derives from Latin Brittonem ("a member of the tribe of the Britons"). That Latin word comes from *Britt-os, which is the Celtic name for the Celtic inhabitants of Britain and southern Scotland before they were driven out in the 5th century. In Old English the country was called Brytenlond, which meant "Wales." In the 4th century, Greeks called them Prittanoi ("tattooed people").
Another possible etymology exists, which is that Britain comes from Old Welsh Priten from Celtic pryd ("countenance, image, beauty, form"). This explanation is problematic though because the change from a word-initial 'p' to 'b' is hard to justify according to normal rules of sound change in English.
Recently it has been suggested that the word comes from a word for "tin" in a Mediterranean Semitic or Hamitic language (confer Egyptian Demotic pretan). The link would have been Phoenician traders who were referring to the most important commodity they bought from Britain. This has come into question because it has also been suggested that the origin of that word for "tin" was a borrowing from the name of the British Isles or its people (taken from Priten, perhaps?).