Without Iwo Jima and Okinawa, the war would have gone on (conventionally fought) for another two years at the cost another two million casualties on both sides.
That's why President Truman authorized the use of atomic weapons. It had to be done.
That doesn't make much sense. Iwo Jima and Okinawa were in U.S. hands before the bombs were dropped. It is true that an invasion of the Japanese homeland would have resulted in at least a couple of years and millions dead.
Clarification: Securing those two islands enabled the continual bombing of the Japanese mainland with escorted B-29's and also secured the seas from any further probability of the Japanese navy interfering with our plans for invasion. They were being used to stockpile the men and materials that would have been needed for the fight; would have been the jumping off point for the armada. Their possession and the ability to spread propaganda knowledge that the Americans were within the borders of the Japanese Empire was debilitating to the general populace and beginning to wear down it's military to the point of inability to fight effectively.
Had Japan been able to hold Iwo and Okinawa, we would probably have had to stage an invasion from the Philippines and continue to send bombers unescorted to the mainland from Guam and the Marianas.
Those were the points of their strategic importance that I was trying to convey in the short form.