Gold, God, and Country. The first explorers came to the Americas in search for a faster rout to Asia. On their journey they found a previously unknown part of the world; and with it, an unknown people and culture. When the conquistadores entered into the great cities of these awesome empires (firstly Tenochtitlan, the capital city of the Aztec empire) they encountered a fortune in gold and new crops that they could take with them back to Europe. Some examples of these new foods included corn, avocados, chilies, vanilla, yams, Chewing Gum, and chocolate.
They also believed it to be their Christian duty to convert the polytheistic natives to their monotheistic Catholic ways.
And lastly, conquering the majority of the Western Hemisphere in the name of Spain ( and Portugal in the case of Brazil) was a smart strategic move that could gain them land, power and more money.