What difference did the Forage War make in the story of the American Revolution?
I assume that you are talking about the time in early 1777 when George Washington attempted to hurt the British by stopping their foraging parties. He believed that he could weaken the British by stopping them when they sent parties out to try to get food and other things they needed for the soldiers and for their animals.
This tactic of Washington's worked in the way that guerrilla tactics tend to work -- they tied down a large number of British troops. Every time the British sent out foraging parties, they had to send troops along to protect them. This meant that those soldiers could not be used somewhere else. It also actually made the problem worse because more soldiers meant more need to forage.
So the main impact of this part of the war was to reduce the levels of manpower that the British were able to dedicate to fighting the war.