Why was the battle of Saratoga an important battle for the Americans?
It showed that the Continentals could defeat a British force in a major field battle, which was important for morale, as well as convincing the French that support of the Americans was worth it. The entry of France as an ally to the Americans would prove to be decisive. More directly, it removed a British army of 9000 men from the field, thus removing a major threat to the mid-Atlantic (and preventing the isolation of New England).