Beneatha is interested in Africa for three reasons: first, she is black, and it is natural to be interested and intrigued by the native country from which the slaves were brought in the early 18th century. Part of the issue with this play is the oppression of the black family (Youngers) in a white neighborhood, so it is all very relevant.
Second, Beneatha is dating a man from Africa. He is intelligent, smart, and good looking. He is also a morally good person and teaches Beneatha some valuable life lessons. The two discuss marrying, and moving to Africa after the two of them complete school is a logical move.
Third, Beneatha's dream is to be a doctor. She often mentions this dream in conjunction with Africa as the country is in need of medical professionals.