There's a lot of different ways that Saratoga affected both the British and Americans in the Revolutionary War. The French joined the side of the colonies due to the similar dissatisfaction with Britain, as well as a very good ally in the trading world too. (However, France would realize their mistake in supporting a Revolution because not long after they would soon have their own Revolution.)
It was a turning point in the war due to the lifted morale of the soldiers, as well as ensuring that support for America would be guaranteed.