Excellent answer. The Portugese, of course, were moving into the area in which the story takes place because of the Treaty of Tordesillas, in which the entire unknown world was divided between Portugal and Spain. The arrogance of these countries in assuming ownership of most of the world and the cruelty in which they carried out their occupations are prime examples of the abuses of power by more developed nations over others.
Portugal and Spain both being seafaring nations and exploring the "New World", both east and west,before other European nations naturally came into conflict. The idea behind the treaty was to solve the potential problem before there was enough exploration to perhaps lead to war. The pope of the day, Alexander VI, was Spanish, and his answer to this political crisis was to simply draw a line on a map and award Spain half the world and the other half to Portugal. Signed in 1494, the Line of Demarcation was some 370 sea miles (leagues) to the west of Cape Verde. The forced conversion and slave labor of native populations by the Spanish and Portuguese resulted in entire peoples being wiped out, such as the native Jamaicans and other Carib Indians.
The story per se has nothing to do with US history, although the arrogance of one nation deciding what is "best" for another people elsewhere in the world does have an obvious lesson for us today.
The film deals with a Spanish Jesuit priest who enters the South American jungle in the hope of establishing a mission to convert the indigenous people of the region to Christianity. The priest, convinced of the authenticity of his convictions, converts a slave catcher who has committed the sin of killing his brother, and together both of them work towards the establishment of the mission. After Spain reaches a land distribution with Portugal who seeks to control the territory once the treaty has been signed, both men have to defend the mission against the marauding forces of the Portuguese.
The film's primary link to the history of the Americas reflects the theme of colonization. European nations viewed lands in Asia, Africa, and South America as extensions of their dominions and sought to control these areas in the forms of religious, political, and social imposition. Imperialism was viewed as a form of "enlightening the natives." The forced conversion of the indigenous people to Western religions would confirm this, as would the enforcement of Western norms regarding trade and political order. The Jesuit priest genuinely believes that he is doing "God's work" in his role in converting the individuals native to the South American jungle. When the Portuguese enter, looking to take over the mission, it is inferred that he understands what it means to be under siege from a foreign power- the colonizer has become the colonized. If there is any implication with U.S. History, it would be that there is a very precarious balance between seeking to expand one's borders and taking over another's.