Here's something from a site:

Africa comes from the name of the Roman province Africa, which was in the Karthago area.

America, that is parted in two - South America and North America, is called after the Italian merchant seafarer and explorer Amerigo Vespucci. The word was used the first time 1507, when the German geographer Martin Waldseemüller named the area in his work "Cosmographiae introductio".

Asia comes probably from the Assyrian word "acu", which means "in the east".

Australia finds its origin in the latin word "australis", which means "southerly". Maybe you've heard about Terra Australis (incognita), that means "(the unknown) land in south". This aims at that Australia once was an unknown, southerly placed land.

Antarctic zone is created from the Greek word "Antarktikas", that means "Right opposite of the Nordic".

And at last:

Europe, which isn't start with an A. Europe's origin is much discussed, maybe it is Greek or maybe it is Semitic. Its means is believed to be "the land of the sunset".


http://www.linema.com/screenplace/continents.html

I googled: "Names of continents" plus "etymology"

Best regards,
WW

P.S. Thanks for a great question!