Politically, the colonists after 1763 became more and more committed to the ideas of Enlightenment philosophy, including the concepts that "men" were born with natural rights that were given to them by God and thus "inalienable" (couldn't be legitimately taken away) and that "the consent of the governed" was the basis of government. As the 1770s wended along, the idea of republicanism also gained more and more traction. This had nothing to do with a political party but was the idea that governments could be created from democratic elections in which leaders were chosen by the people. This anti-monarchial theory was in radical opposition to the British, who were wedded to monarchy.
Socially, as more and more Americans were born in the colonies of families that had lived in North America for generations, ties with and feelings of allegiance to Britain began to fade. This, coupled with the immigrants who came from other countries, such as Germany or Holland, weakened the connection between the colonists and Britain.
The economic differences between the colonies and England diverged markedly after 1763 and was a key trigger point in starting the American Revolution. The Americans wanted to be left alone, as had long been the case, to run their economy as they saw fit. This policy, called "salutary neglect" had benefited both the colonies and Britain for many years. Now, however, Britain wanted to recoup some of its expenses from the French and Indian War. The war had been vastly expensive, and the English naturally felt the Americans, who were the chief beneficiaries of it, should help pay. The Americans felt quite differently and balked at anything that looked like an extra tax or anything that might incite more taxes.
In all these areas, the colonists wanted to loosen ties with the British and become as autonomous as possible. The British wanted to strengthen ties, stay in control, and earn money from the colonies. But after the French and Indian war ejected the French, ridding the colonists of a threat of a French takeover, the colonists no longer needed the British.