Flanders

In Roman times, the area was inhabited by Romanized Celts. Then more and more Gothic Germans came to live there, and in the 3rd and 4th century A.D., the Salic Franks came from the north and drove back the Romans to approximately the area that now divides Flanders from the French speaking part of Belgium, where the Walloons live.
In the 5th century, the Roman garrisons left, and the Franks pushed on further south. The ones that went south adopted the language that was spoken there, which has become what we now know as French, but the Franks that stayed in the north retained their Germanic language, what over the years has become what we now know as Dutch. This is why in Flanders they speak Dutch, and in the south they speak French.

The second - and by far more common - use of the word 'Flanders' is to indicate the part of Belgium in which Dutch is the official language. This is roughly the northern half of Belgium, and includes the provinces of Flanders, Antwerp, Limburg, and part of Brabant. Belgium is now a federal state; Flanders has considerable autonomy, its own government and parliament.