It is believed that there once was a gigantic continent called Pangaea. The first person who had this theory was Alfred Wegener, who thought that 250 million years ago, all the continents were together in one big continent, which he called Pangaea, which was the Greek word for "all the earth". Continents do drift apart very slowly, so Wegener concluded that over millions of years at the same speed, they got to the places where they are today.
At Alfred Wegener's time, no one believed him because they didn't find any evidence for his theory; but Wegener soon found the same type of fossils on the African shores as on the South American shores; and Africa seemed to fit together with South America, so he concluded that he was right.
As more people found convincing evidence that Pangaea existed at one point, the theory became widely accepted. Pangaea may or may not have existed, but there is no biblical evidence that it did not. If Pangaea actually existed, it would have probably come apart during the flood, not millions of years ago.
One of the flaws in Wegener's theory is that he assumed that the continents moved at the same rate all the time. A better explanation would be that a cataclysmic event (the Flood) would have increased the speed of the separation.