I know north Africa got its name during the Roman empire and the region has long historical ties in the classical period. But how far south did these ties stretch? Is there evidence that central or western Africans knew anything about the Mediterranean world and their civilizations? What about vice versa?
There's no firm evidence of knowledge regarding Central Africa or West Africa and the Mediterranean; although a lot of African oral histories and folklore call out to the Classical world, they appear to do so as a means of establishing veracity, via elements incorporated from colonial or Islamic education systems and not something pre-existing. Similarly, there's some connection of Berbers and the like in the Sahara, and they did start crossing regularly again in the very latest imperial period, but we have next to nothing about transfers of knowledge.
That said, there is one area where Rome was certainly known in ancient Africa south of the Sahara: the Nile Valley and the Horn, and perhaps as far south as present-day Tanzania or Kenya. The Periplus of the Erythrean Sea (Red Sea, really) does mention trade out via that sea to spots on the African coast, including the entrepots of Adulis (for Aksum) and Rhapta (on the later Swahili coast); Roman Egypt's Christianity was the root of Aksum's (via Adulis), and so on to Ethiopia's. Inland, the kingdom of Meroë was located on a fork of the White [between the 5th and 6th cataracts of the] Nile, and produced high quality iron while factoring luxury goods (ivory, feathers, precious stones, metals) from further south; at its height, right around the first century CE, Rome and Meroë had a series of sharp military encounters in the Nile valley, with the Romans usually coming out on top but no lasting conquest coming out of it. In any case, the major trading center on Elephantine Island existed precisely to handle trade and relations to the south and the African interior.
It's impossible to know how much we can trust the few accounts (Herodotus, etc) claiming knowledge of areas further south than Meroë, and we have nothing that I've seen about areas to the north that's survived from south of those places. (We're not even 100% sure where the southerly port of Rhapta was--it is most likely covered by some other city at this point, whether Mogadishu, Mombasa, Dar, or something else.) At the very best, it's heavily filtered information that's been badly skewed from whatever it was before. I've written on the supposed voyages of Hanno and the "circumnavigation" of Africa that is claimed from time to time, but there's no corroboration that these things ever happened, and their content is muddied at best. From the side of sub-Saharan Africa, there is nothing that is contemporary, even though mostly durable goods from the north did reach areas to the south and vice-versa. Anything more would be speculative--although if any of our Classicists know something new and exciting, I would love to be wrong about this one.
[edit: corrected horribly flubbed location of Meroë, thanks to /u/camellad]