The significance of the Battle of Bunker Hill during the American Revolutionary War lies in its demonstration of the American Continental Army's resolve and capability to challenge British forces. Fought on June 17, 1775, it was one of the early major battles and proved costly for the British, despite their victory. The heavy British casualties highlighted the determination and fighting spirit of the colonial troops, boosting morale and support for the revolutionary cause. This battle also underscored that the conflict would be protracted and bloody, prompting further colonial enlistment and commitment to the fight for independence, marking a pivotal moment in the war.