There are many important topics you could address in an essay on the American War of Independence. One potential essay topic is the causes of the war. What pushed the American colonists, who were once loyal British citizens, to declare their independence with the Declaration of Independence in 1776 and then to fight a long war to break away from the greatest empire of the day? The answer to this question has been debated by historians, and the answer is partly political and partly economic in nature. The colonists were angered by the British crown's enforcement of the Navigation Acts, which made the colonists import all finished goods from their mother country. These acts also hurt colonial merchants, which was the economic reason that many colonists decided to revolt. In addition, colonists who supported the revolution cited political ideas of the Enlightenment, including the social contract that a ruler had to respect the "inalienable rights" (rights that cannot be taken away) from the governed.
You might also write about the consequences of the War of Independence. While the American Revolution created a government that more closely resembled a democracy than any government to date, the revolution failed to create freedom for many groups. These groups included slaves, women (who did not get the right to vote), and Native Americans (who were regarded as separate, sovereign nations but who were not considered citizens). Your essay might look at the ways in which the American Revolution was, in many ways, not a complete revolution in the social order.