This is the largest hill on the Charlestown peninsula, and the closest to the mainland.
During the Battle of Bunker Hill rebel reinforcements arriving on the Charlestown peninsula headed to Bunker Hill, but weren't sure what to do once they got there. Rather than joining the battle - which was raging on Breed's Hill, nearby - they wandered aimlessly around Bunker Hill, so disorganized they hadn't even brought a picnic.
Israel Putnam was here attempting to direct troops - giving valuable instructions such as the famous "Don't fire until you see the whites of their eyes" (Which he probably said several times, to anyone who'd listen, and to be fair, it's a pretty great quote). That seems to be the only one of his directions that stuck - many of his other orders were either misunderstood or deliberately disobeyed. Given the disorganized state of the Continental Army at the time, it was probably a little of both.