In a word, Inspiration! The Battle of Bunker Hill (technically on Breed's Hill in Charlestown, MA) occurred on June 17, 1775 when General Gage, the British Commander, unwisely ordered a frontal attack on the colonist's makeshift, but strategic fort overlooking Boston Harbor.  The British, the most powerful military force in the world at the time, were to engage the poorly trained and equipped colonial militia.  Although not the first armed conflict between Colonist and Briton, this battle proved to be one of the bloodiest in the war.  The Colonists, outnumbered and outgunned, were eventually forced to retreat, and the British took the possession, but only after suffering nearly 1100 casualties to the Colonist's 400. Although a shocked King George responded by declaring the colonies in a state of rebellion, the most important significance of the battle was the realization by Britain that they were in for a long hard fight, and concurrently, the inspiration created among the Americans by realizing their volunteer militia inflicted nearly 3 to 1 casualties on the best army in the world. The battle gave the Americans the will to take on the British, and possibly even win! "Win the Battle, Lose the War."

Encyclopedia Britannica, 11th ed., vol. 4,  pg. 799. 

Prior to the Battle of Bunker Hill ( Breed's Hill) the British were unsure of their combat status. Was the crown at war or was it an isolated occurance in Boston??? Make no mistake, during The Battle of Bunker Hill, the colonials in Boston were at war with England. The Patriots paid dearly for their principles, however the Patriots delievered severe blows on the British. As a result, The Battle of Bunker Hill if for nothing else, informed King George that there was a fight, and the Continential Congress was not about to concede.