The concept refers to almost all superhero comic books made after Marvel Comics came on the scene with The Fantastic Four and Spiderman. Prior to the "Marvel Age", superheroes were like gods...virtually indestructible and almost always infallible. With the introduction of Marvel characters, there was a more humanistic approach to the characters as we could see that they had similar fears and insecurities as the rest of us, plus a host of personal flaws. Spiderman was young and cocky, Iron Man was a drunk, Hulk couldn't control his rage, etc. This approach slowly found its way into DC Comics and their characters, including Superman and Batman. The high point of all of this was the release of "The Dark Knight Returns" and "The Man of Steel" in 1986. Both examples were true instances of a demythification of the superhero as it showed that the characters that were loved for generations could not possibly be so infallible after all. Superman couldn't save everybody everytime...Batman had a conflicting and almost psychopathic dual personality.
However, this whole concept was probably best explored in the 1995 miniseries "Kingdom Come" where the whole idea of new gods and mortals was reviewed in a beautiful story and artwork.