The Old World is the three continents, Europe, Asia and Africa, whose people knew about each other from ancient times.
Humans originated in Africa, but modern history is mostly about European history. This is because the Europeans wrote more history. For a long time "history" meant the history of Europe and the Middle East. That is still the kind of history which is taught in many schools. Having history depends on having writing. The first writing we know of comes from the Middle East, and the Chinese claim they also had early writing.