The Great War for Empire is more commonly known as the Seven Years' War or the French and Indian War. It had a profound impact on the balance of power between the French and English in North America.
Before the war, the French and English had similar amounts of power in North America. The British controlled the 13 colonies while the French had much of what is now Canada as well as huge amounts of territory (albeit unsettled) in the Mississippi River drainage area. After the war, the French were completely ejected from North America, losing all power on the continent.
Overall, the war (which was waged in other parts of the world as well) ended with British gains. For example, the British were able to compel the French to destroy all fortifications in French territories in India. This gave the British much more power in that part of their empire as well.
This war was a major success for the British and increased their power relative to that of the French worldwide.