The broader sense of revolution began much earlier, continued after the peace treaty, and had a much greater impact on the human experience than simply colonial independence. The process created a new view of government and its organization that the world hadn't seen before. The terms republic and democracy had been used in histories of ancient Greece and Rome, but now they was implemented in a government whose authority was based on individual rights rather than on church or king. While earlier historic trends affected it, the revolution itself had its active roots in the Albany Congress of 1754 and ended when George Washington was sworn in as the first President of the United States in 1789.
Before the revolution most people in the British North American Colonies considered themselves loyal subjects of the British Crown, with the same rights and obligations as people in Britain. However, under the doctrine of mercantilism the British considered the Colonies more as a resource to be utilized for the benefit of their own economy and had little respect for the Colonists. This difference in perception led to a vicious cycle of Colonists acting against what they saw as unfair policies, harsh British reaction, followed by stronger Colonial reaction, leading to even harsher British reaction -- all of this spiraling into the revolution.
As the Colonists started rejecting the Crown they also started becoming more radicalized in other ways, paying more attention to the idea of a broad democracy, and people like Thomas Paine who not long before this would have been condemned as a Leveller. Thomas Paine, produced a pamphlet entitled Common Sense arguing that the only solution to the problems with Britain would be Independence.
See also: American exceptionalism, Boston Massacre, Boston Tea Party, British North America, The Enlightenment, Industrial Revolution, Proclamation of 1763, Stamp Congress, Thirteen colonies, Thomas Paine