The origins of the name 'Africa' are not entirely clear. We get the word from the Roman province gained via their first conquest on the continent. Romans used the term 'Afri' to refer to the inhabitants of Carthage, and more specifically a native tribe of Libya.
In order to facilitate trade, especially of the agricultural variety, various emperors set up colonies along the North African coast. Rome had the people, but the people needed bread. Africa was rich in fertile soil and became known as the 'granary of the Empire.'