Cornwallis surrendered on October 19,1781 because the Americans had double the amount of soldiers than the British.
The British surrendered on October 17, 1777 and it was a major turning point in the war. Once the Americans won the French entered the war against Britain.
In the winter of 1777-78 the Americans trained in the harsh winter conditions and on June 1778, the Americans attacked the British at Monmouth, New Jersey causing the British to retreat. This was the last major battle in the North.