They knew the land better than the British, they had people fighting for a cause they truly believed in (I know it sounds silly but they were fighting for their independence and really gave it their all while the British did not really take it seriously until it was too late, and the Americans had strong leaders (again its a silly thing to say but the strength of men like Washington and Jefferson really helped the morale of patriots). Also after Saratoga other European powers decided to join in on the side of the Americans because they wanted Britain to lose some of its power plus Britain was also occupied with various wars in Europe, some related to the Americas and some not. Hopefully this gave you what you needed.
