The easiest way to explain super heroes is to turn the radio up whenever anyone asks about it.
Why, indeed. First, you need to figure out what you’re explaining. Are you explaining why super-powered beings exist? Or why they seem to exist in such large supply on Earth? You’ll need to think about the future. Will there be as many super heroes around in the future as there are now? Were there so many super heroes around in the past?
Of course, garbage in, garbage out.
An Outside Experiment: Humans are the result of experimentation by an outside individual or group. These can be extra-dimensional, extra-terrestrial, or extra-universal. Or whatever. Usually, the experiment is a genetic experiment, but it’s not necessary. Humans could be part of some great, organic computer, and super heroes are part of the data being spewed out.
Punctuated Evolution: One real-world theory of evolution postulates periods of relative genetic stability, punctuated by short, rapid bursts of genetic change. While this theory hasn’t much of a following in the real world, the sudden presence of super heroes can give it added status in yours.
The Superhero Anomaly: There is a physical anomaly somewhere near the Earth. This anomaly is often a space/time and an astral anomaly. This explains the weird mutations in genetics, as well as minor alterations to the basic laws of physics. It also allows those annoying space warps that bring so many aliens into the area. If you use this option, add 1 (or more) to the space/time continuum and/or the astral continuum, in the area of Earth and our solar system.
The Supernatural: Something beyond normal science is creating super-heroes. Various supernatural beings are blamed, including God, the Devil, and various specific pantheons.