Many historians feel that the Battle of Saratoga was a turning point in the war because it showed the French that the Patriots actually had a shot to win the war. The relationship with France changed our fate in the war completely.
France had been a covert ally prior to the battle by supplying weapons and war material. The Battle of Saratoga brought them in as full partners in the war and also brought Spain in as supplier of weapons and financing.
Saratoga established US control. It is often viewed as a turning point of the war, as it was after this battle that Benjamin Franklin was able to convince the French to ally with the United States to help the colonies win the war.