The quote is the order given to American troops at what is called "The Battle of Bunker Hill" The British were advancing uphill and the Colonists holding the high ground were short of men and ordnance ...therefore : The order "Don't shoot 'till you see the whites of their eyes" meaning do not fire until you were sure you had a clear target at close range.
Before all you historians get on my case...I know the battle was actually fought on Breed's Hill outside Boston ... a monument tower marks the place ... climb the interior circular stairs (unless you're claustrophobic) for a geat view.