There is no objectively correct answer to this question. People could argue for the importance of more than one battle in this war. I would argue, however, that the Battle of Saratoga was the most important battle of the war.
The colonies were, of course, much weaker and poorer than Britain was. This meant that it would be very important for them to gain support from foreign countries. France was the most likely ally in the war. France was Britain’s archenemy and would be happy to see Britain harmed economically and in terms of prestige. If they wanted to, the French could help the Americans economically and militarily.
The problem was that the French did not think it was a good idea to help the colonists. They did not want to needlessly antagonize Britain by backing the American colonists in a doomed war. Therefore, they did not fully support the colonies at the start of the war. This is why Saratoga was so important. It represented a major victory by the Americans. When the Americans won, it convinced France that the colonies could actually win the war. This led to full French support for the colonies. For this reason, it was the most important battle of the war.