The top portion of the earth is made up of gigantic pieces of rock called tectonic plates. Both the continents and the oceans rest on top of these plates. Underneath the plates lies a mass of melted rock. The plates float on this liquid. If a plate moves, so do the continents and oceans which lie on top of it.
Some continents straddle more than one plate.
If two plates on which a continent rests move apart, the continent is ripped in two. Part of it stays on one plate and one part moves away with the other. This is what happened to America, Africa, and Europe. They used to be one single continent. Then the two plates on which this continent rested became separated.