Old World is a term about the three continents, Europe, Asia and Africa, whose people knew about each other before Christopher Columbus.
They had foods and animals Native Americans had not seen before, like sugarcane, pigs, and horses. But, they did not know that they were also giving sickness. They accidentally killed many Native Americans. They also killed many of them on purpose, in conquering them.
The people of the Old World called the Americas the New World.