Why were Europeans interested in colonizing America?

The Europeans were interested in colonizing America because of prestige, religious conversion, natural resources, and land expansion. The French, British, and Spanish empires were major colonizers in the Americas. Spanish conquistadors explored the Americas in search of gold and other resources throughout the sixteenth century. Due to meager inheritances, many noblemen who were not the eldest sons of their families set sail for the New World to gain high status and additional income. In addition, the Spanish used their colonies to convert the native people to Christianity.
French missionaries were interested in conversion as well, but France’s leadership was more concerned with trade efforts. Explorers claimed New France in 1534, and although colonization efforts failed in the beginning, the fur trade with the natives became a lucrative venture. The British also grew interested in North America and competed with the French for commerce and territory. The British crown intended to exploit raw materials in North America and open additional markets for English products.
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The primary reason the European countries were interested in colonizing America was for the vast resources that were available within America. The vast resources of America included furs, lumber, fish, and sugar. These resources were in high demand in Europe, and the abundance of them in America, allowed them to harvest the resources for sale in Europe.
Another reason the European countries wanted to colonize America was to spread their cultures and religions to the "savage" people that inhabited America. They wanted to teach these different cultures, who they deemed to be inferior, how to be like them, act like them, and have their same beliefs.
The Europeans also wanted to have a new land where they could have people come to, help with overcrowding within their own lands. This also allowed the Europeans to send some of the people they view as trouble makers, criminals, or undesirable off to the New World to help colonize it. This ended up being beneficial for the people labeled as such and for the homeland as these people were no longer in their country.

The main reason was undoubtedly economic. America held out the tantalizing prospect of vast deposits of mineral wealth. Legends had abounded in Europe over the years about the enormous riches that could be found and exploited in the New World. With European economies going through the inevitable cycles of ups and downs, it seemed like a good idea to explore an alternative source of wealth that would at least minimize economic disruption during a downturn.
Europeans also believed in their cultural superiority and thought that this entitled them to spread the "benefits of their civilization" far and wide. They didn't know a great deal about America's indigenous population, and what little they did know was shrouded in legend and myth. But the Europeans were convinced that the native population consisted of heathen savages who needed to be "civilized" by a more "advanced" race.
Allied to the Europeans' self-image of cultural superiority was the belief that their religion, Christianity, was superior to what they regarded as the dark, savage practices of the indigenous population. Many of those involved in the colonial project genuinely believed they had a God-given duty to spread the Gospel to the remote parts of the globe, converting what they saw as the poor, benighted natives to the one true faith.