How did the capture of Iwo Jima make the defeat of japan more likely?

Answer 1

Iwo Jima is only about half as far from the Japanese home islands as the islands of Guam and Tinian,

and it would have been a major staging area for the invasion of Japan itself. The loss of the island demonstrated the inability of Japanese armies to stop the advance of US forces. At the same time, it suggested that the resolve of the Japanese was to win or die, and figured in the eventual decision to coerce a Japanese surrender instead, using atomic weapons.

Answer 2

The loss of American lives in capturing Iwo Jima made the prospect of capturing the Japanese inner islands a very, very daunting prospect in the projected loss of American lives. Whether you agree or not, the bombing of Hiroshima and Nagasaki (horrible as it was) at least forced the Japanese to finally give up!