The first years of the Revolutionary War were discouraging for Americans. British forces were larger, better trained, and better equipped. American victories were few, but in the fall of 1777, Americans defeated the British in two battles that turned the war in their favor.
In the summer of 1777, the British army under General John Burgoyne moved south towards Albany, New York. Burgoyne planned to gain controls of the Hudson River and separate New England from the other colonies, but about 25 miles north of Albany, at Bemis Heights, an American force under General Horatio Gates blocked his path. The British tried twice to get around Gates. On September 19 and again on October 7, the armies clashed at Freeman’s Farm, a mile north of Bemis Heights. The Americans were victorious both times.
Burgoyne pulled back to Saratoga (now Schuylerville). He expected help from British forces in southern New York, but relief did not arrive. The Americans surrounded the British, and on October 17, Burgoyne and his 5,000 men surrendered. The victories near Saratoga gave Americans new confidence and convinced the French that Americans had to resolve and skill to defeat Britain. As a result, France entered the war as an American ally.
One of the heroes of the Saratoga campaign was Benedict Arnold, who later betrayed the American cause.
The image you see here is a painting by John Trumbull titled The Surrender of General Burgoyne, and it hangs in the Rotunda of the United States Capital.