The Battle of Saratoga ranks among the most important turning points of the Revolutionary War, but its greatest importance lies in its diplomatic repercussions, which had the effect of fundamentally transforming the nature of the conflict.
Ultimately, what you must remember is that in the American Revolution, the colonists were at a disadvantage facing the British. They had limited formal military expertise and were facing the British army (note also that the British employed mercenaries as well). Moreover, they had no answer to British naval supremacy. Winning their independence in a sustained military conflict represented an extraordinarily difficult, uphill struggle.
At the same time, however, the American Revolution unfolded within the context of European political rivalries, and the other European powers were watching the Revolution, a fact of which the Revolutionaries themselves were well aware. Nations such as France had a vested interest in seeing the colonies successfully break free from Britain and wished to avenge earlier humiliations against the British. The question was, for them, a matter of viability more than anything else. Did the American Revolution have a real chance at success?
The Battle of Saratoga's importance lay in the way in which it answered that question, as the colonists handed the British a decisive military defeat. In the aftermath of this victory, France would sign a formal alliance with the United States. The entry of another European power radically transformed the picture of the Revolutionary War, in ways that would prove critical in ensuring its success.