The New World is a term for what is now largely known as the Western Hemisphere. The term originated in Europe in the late 15th century to describe what were largely unknown and uncharted lands to the west, the Americas. Spain was the leader in the explorations (which quickly turned into conquests, also explaining why now South America primarily speaks Spanish) beginning with Christopher Columbus. England, France, and the Netherlands soon followed suit.
These first-world, military powers were not the first people, nor even the first Europeans to discover these lands, so the term mainly belongs to Europe-at-large's initial awareness of other continents on Earth.