Why was the battle of Iwo Jima significant in the grand scheme of the war itself?
There are those who would argue that this battle really was not significant in the grand scheme of the war. They would tend to argue that this was a battle that was undertaken not because it was really necessary, but because of interservice rivalry. The article in this link, which is written not by an anti-war person but by a Marine who has taught at the Naval Academy, persuasively argues that it was really not important to take Iwo Jima. I tend to agree with it.
If we say that the battle was important in the grand scheme of the war, we must argue that it was an important way to ensure that the US would be able to engage in strategic bombing of the Japanese home islands. Once Saipan and Tinian in the Marianas were captured, the US had bases from which to fly B-29s to bomb the Japanese home islands. This was an important part of the US strategy for winning the war. The battle of Iwo Jima can be seen as supporting this bombing campaign. It was meant to provide damaged bombers with a place to make emergency landings. It was also meant to be a place from which fighters could take off, meet up with B-29s, and escort them to and from Japan.
This is the significance of the battle of Iwo Jima that is traditionally given in textbooks, even if it is somewhat of a dubious justification for that battle.