Your question is a bit oversimplified because there are many types of supernovae based on the size and configuration of the star. But I can answer your question about "why iron" by considering what keeps a star from exploding in the first place.
In the simplest terms of star formation, when material from an interstellar nebula starts to collapse under its own gravity, the pressure and temperatures involved will become great enough to eventually start fusing hydrogen into helium (it's a bit more complicated than that, but I'm speaking in generalities). If you were to consider the helium atoms created by that process, you'll notice that each helium atom weighs just a bit less than the two hydrogen atoms that formed it. That bit of extra mass is given off as energy which is produced in great quantities as the hydrogen continues to be fused into helium.
During the star's "main sequence", the release of energy by the hydrogen-helium fusion helps counteract the weight of the star's gasses pushing inward. Material presses in; energy pushes out in perfect balance. This balance of gravity and energy output continues until the star uses up most of its hydrogen.
It's at this this point (when there is no hydrogen to fuse into helium) that the fusion reaction stops and gravity will resume to collapse the star further. As this star collapses, it will quickly become denser and hotter until the temperature and pressures of the interior are great enough to start fusing helium into heavier elements… and the process continues.
That is, until the star starts fusing elements into iron…
The fusion into iron is the first element that does not create more energy than it takes to produce. The effect is that there is no net energy being produced to counteract the gravity pushing inward. So the outer layers will quickly collapse into a much denser and smaller ball causing the remaining star material to undergo fusion all at once, causing the supernova.
So, in that sense, iron is not the cause of the supernova, but its presence marks the inevitable end of this star's life cycle… in this particular scenario.
But understand that this is an oversimplification to illustrate the process you asked about. There are many other sequences of a star's life cycle. Our sun, for example, does not have sufficient mass to keep collapsing down with sufficient pressures to fuse heavier elements into iron. Without getting into other pathways for the production of heavy elements (even in smaller stars like our sun) — once our sun starts creating carbon and oxygen, the fuel starts to run out and the core will simply collapse and rebound as it swells up into a red giant, before losing its outer layers as a planetary nebula while the core shrinks to become a white dwarf (and eventually cooling into a black dwarf).