The term originated in the early 16th century after Europeans made landfall in what would later be called the Americas in the age of discovery, expanding the geographical horizon of classical geographers, who had thought of the world as consisting of Africa, Europe, and Asia, collectively now referred to as the Old World (a.k.a. Afro-Eurasia).
The terms "Old World" vs. "New World" are meaningful in historical context and for the purpose of distinguishing the world's major ecozones, and to classify plant and animal species that originated therein.
One can speak of the "New World" in a historical context, e.g., when discussing the voyages of Christopher Columbus, the Spanish conquest of Yucatán and other events of the colonial period. For lack of alternatives, the term is also still useful to those discussing issues that concern the Americas and the nearby oceanic islands, such as Bermuda and Clipperton Island, collectively.