Colonialism, conquest, and religion are strongly linked in the European imperialist era. Colonialism, to start, was a game of conquest. The motive may have occasionally varied, but it was largely motivated by power or money. In fact, colonialism can be considered an act of conquest motivated by monetary gain since the major point of colonies was to provide an additional source of income for nations. In this way, colonialism and conquest were two sides of the same act.
Religion fits into this as a method of conquest. In one way, it was a way to convince citizens of the home country to participate in the conquest. Beyond those who were motivated by power or money, there were people who were motivated by a desire to spread their religion. Particularly in the Spanish colonies, it was extremely common for missionaries to be some of the earliest settlers as they worked to spread their religion among the native populations and, a bit later on, among the slave populations that were brought to the Americas.
More than this, however, religion was also used, perhaps unintentionally in some cases, as a method of controlling the native population of a conquered area. By converting the native population to the religion of the conquerors, the invaders gained a power over the natives that was not reliant on warfare. In effect, it became a method in which the native population, by converting to the conquering religion, gave their conquerors power over them. For example, if a member of the Incan civilization converted to Christianity after the Spanish conquest, that meant that this Incan was subject to the rulings of the church. So, in addition to having military power, the Spanish conquerors would have religious power over the converted population of the conquered. Because of this complex system associated with imperialism—particularly European imperialism—colonialism, conquest, and religion were tightly linked.