Final answer:
Christopher Columbus discovered the Bahamas, Hispaniola, and Cuba, mistakenly believing them to be part of Asia. He established a settlement and initiated European contact with the native peoples he called 'Indios', marking the beginning of Spanish exploration in the New World.
Step-by-step explanation:
When Christopher Columbus and his men discovered land on October 12, 1492, they first encountered an island in what would later be known as the Bahamas. Their exploration thereafter led them to the larger islands of Hispaniola and Cuba in the Greater Antilles of the Caribbean. Columbus initially thought he had reached Asia and described the area as a tropical paradise, lush and ripe for Christian conversion and exploitation. Upon his return to Spain in 1493, Columbus brought back gold and valuables that convinced the Spanish crown of the richness of these lands. Columbus named the native peoples he encountered "Indios," erroneously believing he was in the East Indies. The settlement established in Hispaniola, Fort Navidad, was the first European establishment in the New World, though Columbus found it destroyed upon his return on a subsequent voyage.
Columbus's belief that he had reached the East Indies guided his interpretation of his discoveries, yet his voyages ultimately revealed the existence of the Americas, a whole new world previously unknown to Europeans. His encounters with the native Taínos and subsequent designation of them as "Indians" left a lasting legacy. Despite later explorations, Columbus went to his grave believing he had landed on the outskirts of Asia, although future explorers would eventually realize the true nature of the continents he had stumbled upon.