Great question! The answer has to do with the force that keeps atomic nuclei together. You probably know that the nuclei of atoms are made up of protons and neutrons, which together we call nucleons. But protons are positively charged, so the electromagnetic force should make them fly apart - it turns out there's another force (called the strong nuclear force) which takes over when the protons are really close to each other and makes them attract instead of repel.

Now, this means that there is some energy associated with the protons and neutrons getting "stuck" together - this energy is called the nuclear binding energy (technically, the nuclear binding energy is the energy it would take to break a nucleus up into all of its separate protons and neutrons). It turns out that the binding energy per nucleon varies depending on the size of the nucleus (and therefore the kind of element you're considering), and the element with the largest binding energy per nucleon is iron.

That means that if you have an element lighter than iron, you can get some of its nuclear binding energy out by fusing the element into something heavier. Likewise, if you have an element lighter than iron, you can get some binding energy out by splitting it (that is, having it undergo nuclear fission) into something lighter. But once you get to iron, you're done - you can't get any energy out of iron, either by performing nuclear fission or fusion!

The most stable isotope is iron-56. Anything lighter than that will release energy as it is fused to make heavier elements. Anything heavier than that will release energy by being broken apart into smaller pieces. Turning iron-56 into anything else consumes energy, as you would expect. I don't know what it is about iron-56 that makes it more stable than any other isotope.