As pointed out in the text section you showed, three key reasons the Americans were successful in their fight for independence were:
They fought on their own land and knew the local terrain, which gave them tactical advantages over the British. They were fighting for their home turf on their home turf. They had "home field advantage," in a sense, knowing the geography better than their British adversaries.
They received help from other nations -- directly from France and indirectly from Spain. The American side received an especially large advantage of financial support and military support from France as an ally, which strengthened their side against the British. General Lafayette was one of the key French leaders who assisted the American war effort.
The Americans were fighting as a people for a cause they deeply cared about. They were highly motivated, fighting for their independence as a nation. They also knew that if they lost, the penalties for treason against the British were worse than death in battle.
A couple other advantages the American side had, which were not mentioned in the excerpt you showed:
Use of an outstanding spy network to gather intelligence on British troop movements.
Use of innovative tactics of warfare, such as snipers.
George Washington's decision to inoculate the whole army against smallpox in 1777. Smallpox was a major killer of soldiers on both sides in the war. Washington's bold move to inoculate all his troops gave the colonists an advantage.
