The Great War for Empire is more commonly known in US History books as the French and Indian War. The British victory in this war helped lead to the American Revolution in at least two major ways.
First, the British victory made it so that the Americans no longer needed to fear the French presence in what is now Canada. This made it more likely that they would feel that independence was a viable option. Previously, an independent America might likely have been snapped up by the French coming down from Canada.
Second, the British victory led to more taxes and more regulation of the American colonies by the British. The British government felt that they should be getting more out of the colonies, economically speaking, to help pay for the war. By imposing new taxes and regulating the colonies more closely than it had before, Britain drove the colonists to resent the mother country and, eventually, to fight for their independence.