What are some reasons the European settlers came to America?

European settlers were motivated by "Gold, God, and Glory." They had economic, religious, and social reasons to settle in the New World.
Trade and the acquisition of wealth motivated them. In the fifteenth century, trade with Asia and access to Asian spices were important. However, it was difficult for Western Europeans to access Asian trade directly. Therefore, both Spain and Portugal sought new routes to the East Indies. Portugal eventually made it by going around Africa. Spain tried going West with Columbus's voyage. Spanish 'conquistadors' (conquerors) led the way in the New World. They subdued the Aztec and Inca empires. The Spanish were ruthless and avaricious, and they acquired gold and silver. Indians were killed by their guns or diseases. Later, both France and England acquired land in North America and engaged in trade. New France had a fur trade.
Religion was also a powerful incentive. Priests went to New France to convert the Indians. Spanish priests accompanied the conquistadors. Prior to 1492, Spain was defeating the last Muslims on the Iberian Peninsula and spreading Christianity to newly conquered areas. Spain continued this pattern in the New World. In English North America, the religious motives were different. The English were not converting many Indians. But many English settlers went to North America in search of religious freedom.
Glory was also an incentive for both individuals and nation states. Spanish conquistadors came from a humble background, and they knew they could become fabulously wealthy and acquire status in the New World. Nations also wanted to enjoy the prestige that came with the acquisition of empire. For many men, there were few opportunities in Europe, so undertaking a difficult voyage to the New World often seemed worth the risk. Nation states had the resources to underwrite their voyages.