This obelisk commemorates the battle of Bunker Hill, which wasn't fought on Bunker Hill at all. Colonial forces fought British soldiers on nearby Breed's Hill. Although they were finally forced to retreat, the Colonials managed to inflict heavy casualties on the British.
You can visit the Monument's small museum and climb up the 294 stairs inside the obelisk for a view of Charlestown and Boston. Unfortunately, there's no elevator.

