Afri was the name of several peoples who dwelt in North Africa near the provincial capital, Carthage. The Roman suffix "-ca" denotes "country or land".
Other etymologies that have been postulated for the ancient name 'Africa':
the Latin word aprica, meaning "sunny";
the Greek word aphrike, meaning "without cold." This was proposed by historian Leo Africanus (1488-1554), who suggested the Greek word phrike (φρίκη, meaning "cold and horror"), combined with the negating prefix "a-", thus indicating a land free of cold and horror.