Once Christopher Columbus found and brought back news of the New World, everyone in Europe wanted to go and explore it. Each country that arrived in the New World had their own agenda for coming.
Some countries wanted to create an empire, while others wished to expand their trade routes. Christopher Columbus sailed for the Spanish, looking for a new route to Asia when he stumbled upon the New World. He claimed the land for King Ferdinand and Queen Isabella and traveled back across the ocean for Europe to tell them.
Having conquered all the Spanish kingdoms, the king and queen wanted to augment their empire and sent more ships to conquer and colonize in the New World. Their fleets conquered two powerful Native American tribes, the Aztec and the Inca. The Spanish ended up conquering and colonizing Central America, almost all of what is now South America, and parts of the United States. Unlike the Spaniards who came to conquer and who were cruel to the Native Americans, the French came to the Northern Americas to make new trading posts. The French heard of the furs in what is now Canada and started colonizing and creating their trade posts there. Along with the French people came the Jesuit Missionaries, who tried to convert Native Americans to christianity. Many of the English settlers who colonized in what is now eastern United States came for freedom from religious persecution. After Martin Luther posted his 95 theses about what was wrong with the Catholic church, denominations of Christianity started being created.
The denominations led to persecution among religions in Europe. Many people sought solace from the persecution in the New World. These were only a couple major reasons for exploring and colonizing in North America, although there were more like economic reasons. It all started when Europe was trying to find a new route to Asia, and Christopher Columbus came up with the idea of sailing west to get there. He stumbled upon an island in the New World and now we have America.