Why did the Spanish conquer and colonize the Americas? Young students are typically taught that "Gold, Glory, and God" led to the Spanish empire. But the real answer is probably more complex than that.
A prerequisite for Spanish exploration was the Renaissance. The Renaissance brought Europe out of the Middle Ages and into the modern era. Intellectual pursuits, including the study of geography, were valued. The Renaissance inculcated the Spanish with a curiosity of distant places. The Chinese, on the other hand, chose to eschew voyages of exploration as the Spanish made rapid strides.
Another factor that enabled Spain to establish an empire was its national unity. The Spanish kingdoms of Castile and Aragon were united in 1469. In 1492, the last Muslims on the Iberian Peninsula were subjugated. Because foreign voyages of exploration were so expensive, only a united kingdom could undertake them. By the end of the fifteenth century, a unified Spain was ready.
Trade was an extremely important motivation. East Asian trade had become valuable, and spices from that region were coveted by Europeans. Portugal and Spain sought sea routes to east Asia because overland trails were dominated by hostile Muslims. While Portugal gradually sailed around Africa, Spain decided to reach the East by going West; Christopher Columbus tried to reach Asia by sailing West.
The Spanish reached the Americas, not Asia. It took them years to realize this. In the meantime, they conquered the Aztec and Inca empires and stole huge amounts of gold and silver from the Indians. They killed, enslaved, or converted the Native Americans and built an empire which lasted for centuries.