In the case of Africa and South America, they were once part of a single continent called Gondwana. Gondwana began to break apart around 180 million years ago during the Early Jurassic period. This breakup was caused by the development of a rift, or zone of weakness, between Africa and South America. Over time, the rift widened as the African and South American plates moved away from each other, eventually leading to the complete separation of the two continents.
The movement of the African and South American plates continues to this day, although the rate of movement has slowed down considerably since the initial breakup of Gondwana. As the continents continue to move apart, the Atlantic Ocean between them continues to widen.