The Royal Navy was, at the time of the American Revolution, the undisputed ruler of the High Seas. Though economically strained by debt from the Seven Years War and soon by the expanding nature of the American Revolution, the empire's infrastructure was still stable and relatively sound. Not only that, the British Empire still retained the loyalty of at least a third, perhaps more, of the colonists living in the thirteen North American colonies which revolted.
By contrast, the American colonists were in economic and political disarray. The states were not effectively unified. The national government was largely impotent. Continental currency was practically worthless. The American army was poorly supplied, insufficiently trained (initially), and inconsistently paid.
The reasons Britain lost the American Revolution begin with an understanding of what the British had to accomplish militarily in order to win. King George III and Parliament bulled their way into a military confrontation with the colonies, when a political solution would've been far less costly and much more effective in retaining the loyalty of most American colonists.
Had the British government listened to some of its own members, like Edmund Burke, who counseled respect and conciliation toward "our English brethren in the Colonies," the war could have been avoided. This was not to be the case, however, as British Tories carried the day.
Once war broke out, the British had to suppress the American insurrection and restore their preeminence in North America. To accomplish this, they had to crush any American army in the field and win the loyalty or at least compliance (however reluctant or grudging) of a majority of the American colonists.
The British faced three significant obstacles to achieving those objectives:
1) Their army simply wasn't large enough to occupy enough square miles of territory in North America.
2) Distance. The American rebels had the "Home Field" advantage,...