In the 1960s geologists began to uncover proof that the continents not only float—that is, move up and down within the crust—but that they also travel, or drift, laterally. If you take a good look at a World map, you can see that the continents “fit into” one another. Today, scientists say that continents are moving a few centimeters every year.
The theory was first advanced by Alfred Wegener. It said that Earth’s continents were originally one land mass. Pieces of the land mass split off and migrated to form the continents
Tectonic Plates Movement – Chronology

About 240 million years ago, there was only a single Mega-Continent, called Pangaea.
About 160 million years ago, Pangaea split into two parts, viz, Laurasia and Gondwanaland.
About 140 million years ago, India separated from Gondwanaland and stated moving northwards.
As we see today, all the continents fit into each other. They have achieved this state after millions of years of movement.
This theory is known as the Continental Drift Theory.