The intellectual and cultural movement known as the Enlightenment influenced America in lots of different ways. One of the key components of Enlightenment thought was the belief that everyone was endowed with natural rights which could not be breached by any government. Among other things, this meant that if governments did try to breach such rights, then the people were entitled to rise up and overthrow them, replacing them with governments that would respect those rights.
Indeed, this is precisely what happened in America under British colonial rule. As set out in the Declaration of Independence, the American colonists believed that their inalienable natural rights—to life, liberty, and the pursuit of happiness—had been violated by the British. Therefore, they believed themselves entitled to change the form of government under which they lived, which meant breaking free from the British once and for all.