Why do you think British General Howe wanted to capture Philadelphia?
At the time it was considered the capitol of America. It is where the Continental Congress met.
It is good military strategy to "cut off the head" of the country you are warring with. This can mean the commanding general or that country's capitol.
The British were hoping to demoralize the Americans but what they failed to consider was the fact that American had 13 capitols, each considering itself autonomous which, until 1789, it was.
During the time the British occupied Philadelphia the Americans simply moved the Continental Congress first to Lancaster Pennsylvania then to York Pennsylvania.
For the duration of the war, the Continental Congress's prime consideration was the conduct of the war. Although faith in Washington wavered a little at the beginning, he kept the faith of the Congress in him through 1783.
Governing of the colonies was done at the 13 colonial capitols which means the British did not disrupt the American's conduct of the war nor did it cause the least amount of demoralization. If anything, it coalesced Americans and redoubled American desire.