How did the Battle of Harlem Heights affect the American Revolution?

While it had no strategic effect on the overall conflict, the Battle of Harlem Heights did serve to significantly boost the morale of the Continental Army. The battle itself was not much more than a sustained skirmish between British forces under General William Howe and American forces under General George Washington. Casualties on both sides were minimal, and both armies held the same grounds that they did before the engagement began. In fact, both sides claimed victory; although technically, it was an American victory, as they successfully repulsed the attacking British forces.
What is significant is that this engagement took place after a series of humiliating defeats for the Continental Army, including the disastrous Battle of Brooklyn the previous month. Unlike those other battles, the Continental Army stood its ground and even pressed the fight for several hours against the British advanced lines. This served to boost the morale of the formerly disheartened American soldiers who had never experienced a battlefield success under General Washington before. It showed that the general was able and willing to take the fight to the British and knowledgeable enough to out-maneuver them. Washington himself noted that spirits among his troops greatly improved after the engagement.
So even though the Battle of Harlem Heights did not directly affect the outcome of the war, it gave the Continental Army the confidence it needed to continue the fight against the British. Furthermore, it let it be known that Washington was a capable military leader in the field.