Over Earth's history a number of supercontinents are thought to have existed. The most recent and well understood is the supercontinent known as Pangaea, which formed approximately 335 million years ago and began to break up into the continents we know today, from about 175 million years ago.
It's important to understand that the Earth's crust and it's land masses are in constant flux over geological time. Tectonic plates are shifting continuously and over millions of years this causes land masses to collide and split apart. The way we see the land mass (countries and continents) distributed on a world map today is simply a snap shot in Earth's history. It was a vastly different picture 100 million years ago and will be a vastly different picture in 100 million years. The Himilayan mountain range in Asia is growing today at a rate of about 1cm per year as the Indian and Eurasian tectonic plates continue to collide and thrust up crust material to produce the mountains.
The evidence to support the supercontinent theory is not just in tectonic plate theory, it's in the relationships between life on and between different continents. When land masses split and separated populations of plants and animals, they evolved differently to form new species. The intricacies of these inter-species relationships and genetic heritage can be used to track the nature of how the landmasses interacted over time.