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.