North America
The North American continent existed during the Middle Ages, but it was not known of by anyone outside of the continent until the 11th century, when Norse explorers settled in eastern Newfoundland. In the early 15th century the continent was explored further by the Chinese and then, more famously, by the Italian Christoper Columbus in 1492.
South America
South America, like North America, was not known to anyone but the native population for much of the Middle Ages. There is evidence that the Chinese discovered the continent sometime early in the 15th century or even the 14th century, and it was also discovered by Columbus on later voyages from Europe in the 15th century.
Asia
Asia was a well-known continent during the Middle Ages. Though North American history is very Euro-centric, there were thriving and advanced civilizations on the Asian continent in the Middle Ages, most notably in what is now known as China and India.
Africa
Europeans were well aware of the African continent during the Middle Ages because of its close proximity to the European continent. Much of North Africa was dominated by various empires out of both Europe and Asia, in particular the expansion of Islam from the Middle East.
Antarctica
The theory of an independent southern continent was formulated in the Middle Ages, in the 15th century, but it was not until later, in the 19th century, that the Antarctic continent was actually discovered. Millions of years ago, the Antarctic continent was home to abundant life, but in the modern era it has not been hospitable enough for much life to thrive there.
Europe
Europe, by the Middle Ages, was a well-settled continent with thriving civilizations. The dominant civilization though, the Western Roman Empire, was in decline by the beginning of the Middle Ages and was largely destroyed in the fifth century.
Australia/Oceania
There were many native peoples, known as Aborigines, inhabiting the Australian continent during the Middle Ages, but there was little if any contact with other continents during that time. The book "1421: The Year China Discovered the World" theorizes that Australia and New Zealand were discovered by the Chinese in the Middle Ages, in the fifteenth century.