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.
The term "New World" is used in a biological context, when one speaks of Old World (Palearctic, Afrotropic) and New World species (Nearctic, Neotropic). Biological taxonomists often attach the "New World" label to groups of species that are found exclusively in the Americas, to distinguish them from their counterparts in the "Old World" (Europe, Africa and Asia), e.g. New World monkeys, New World vultures, New World warblers.
The label is also often used in agriculture. Asia, Africa, and Europe share a common agricultural history stemming from the Neolithic Revolution, and the same domesticated plants and animals spread through these three continents thousands of years ago, making them largely indistinct and useful to classify together as "Old World". Common Old World crops (e.g., barley, lentils, oats, peas, rye, wheat), and domesticated animals (e.g., cattle, chickens, goats, horses, pigs, sheep) did not exist in the Americas until they were introduced by post-Columbian contact in the 1490s (see "Columbian Exchange"). Conversely, many common crops were originally domesticated in the Americas before they spread worldwide after Columbian contact, and are still often referred to as "New World crops"; common beans (phaseolus), maize, and squash – the "three sisters" – as well as the avocado, tomato, and wide varieties of capsicum (bell pepper, chili pepper, etc.), and the turkey were originally domesticated by pre-Columbian peoples in Mesoamerica, while agriculturalists in the Andean region of South America brought forth the cassava, peanut, potato, quinoa and domesticated animals like the alpaca, guinea pig and llama. Other famous New World crops include the cashew, cocoa, rubber, sunflower, tobacco, and vanilla, and fruits like the guava, papaya and pineapple. There are rare instances of overlap, e.g., the calabash (bottle-gourd), cotton, and yam, and the dog, are believed to have been domesticated separately in both the Old and New World, their early forms possibly brought along by Paleo-Indians from Asia during the last glacial period.
In wine terminology, "New World" has a different definition. "New World wines" include not only North American and South American wines, but also those from South Africa, Australia, New Zealand, and all other locations outside the traditional wine-growing regions of Europe, North Africa and the Near East.