Our first observation should probably deal with regional differences in religion during the colonial period in North America. New England was the area primarily settled by Calvinists—that is, the Puritans, as those in Britain who adhered to Calvinism were known. In the Middle Colonies and the South, there was either greater dominance by members of the Established Church, or greater diversity including other Protestants or other dissenters such as Quakers and Roman Catholics. Calvinism was therefore merely one religious element out of several in the European settlement of the continent.

But what characterized New Englanders in particular that can be traced to Calvinism? In the popular consciousness, we usually associate Calvinism with what came to be known as the Protestant Ethic. Hard work, success in business, and the accumulation of wealth were considered prime virtues, because Calvin's teachings had apparently indicated that success in "this life" meant that one was of the elect, and that one's fortunes here were a predictor of success in the afterlife. This kind of thinking caused the Puritans to stress not only mercantilism and competition, but the importance of knowledge and education. Even today, the Boston area is considered the educational hub of the US with its unusual number of universities, including, of course, Harvard.

Eventually, much of this competitive and success-oriented attitude trickled down through the colonies, becoming more emphatic after independence was achieved. Yet the extent to which it was due to Calvinism has perhaps been exaggerated. The English themselves already were, among the European nations, more aggressively mercantile and business-oriented, probably because of Britain's status as an island, the necessity of seafaring and trade, and the tradition of independence and (relative) democracy going back at least to the Magna Carta in the early 1200s.

It's debatable whether some special American drive to be "successful" in business and other realms is a Calvinist tendency or is due to other factors, including the random conditions of a frontier country in which the new inhabitants worked hard and achieved success simply out of necessity and not because of religion.

Calvinism asserts the absolute sovereignty of God, arguing that God has something to say about every aspect of life on earth. In other words, God determines the fate of every man and woman, and he might endow some individuals or societies with great prosperity while denying the same to others.

Restrained by existing church doctrine, either Catholic or Anglican, some Calvinists—later called "Puritans"—fled Europe and England in the 1600's to establish what they hoped would be a purified church on the North American continent. This puritanism, originally confined to Massachusetts and some parts of New England, eventually spread throughout the colonies.

These Calvinist reformers believed that America, not unlike Israel, had been specifically chosen to perform God's divine mission on earth. After all, God had blessed newcomers to America with seemingly infinite land and raw materials for which to achieve their goals. Moreover, he had blessed the nation with innovative and competent leaders who, in their wisdom, had devised a free government with a lofty Constitution which provided rights and freedoms to its citizens. These events led many to believe in what came to be labeled "American Exceptionalism."

These blessings, so to speak, led one journalist, John L. O'Sullivan in 1845, to proclaim that it was America's "Manifest Destiny" to push westward and claim the entire continent for the United States. Never mind that many sections of America were already inhabited by Native Americans who also tended to believe in their own sovereignty. Americans, however, true to their Calvinist teachings, believed the natives to be inferior. They did not possess nearly a fraction of the wealth and technology of European Americans and so must be on the proverbial outs with God. In the long run, whether or not the invaders were correct, technology, and the ruthless tactics of American military leaders, led to an eventual capitulation by every native tribe on the continent, much to their detriment.

Today, many Americans still subscribe to the Calvinist world view, especially in a capitalist nation which has economic winners and losers.

This is a good question. There are several important reasons why Calvinism is important to the history of America. 

First, many of the people who came over from Europe to settle in America were Protestant Christians. More specifically, they were Calvinists. They followed the theology that emerged from John Calvin. For example, the Puritans were Calvinist. In addition, the Dutch Reformed church was also Calvinistic in their theology. So, to know our first ancestors, we need to know something about their religious beliefs. 

Second, we can say that Calvinism breeds a certain type of lifestyle. Calvinists believed in a strong work ethic. Weber, the great sociologist, even made a correlation between Calvinism and Capitalism. His point was that Calvinists worked hard and saved and invested. There was a theological sentence that encapsulated this idea:

"Laborare est Orare." "To work is to pray."

Third, some of the greatest minds of early America were Calvinists as well. Two of the most famous people of early American history were Cotton Mather and Jonathan Edwards. They were both Calvinists. So, to some degree, American sensibility even today is Calvinistic.