A consuming self-absorption or self-love; a type of egotism. 
In psychoanalysis, erotic gratification derived from admiration of one's own physical or mental attributes.
Azuma uses the term to characterize the intellectual climate of Japan in the 1980's. The popular theory was that since Japan had never been modernized properly, it was better equipped than Western countries to leave modernity behind and embrace the process of postmodernization. Subsequently, "Japan will emerge in the twentieth century as a leading nation boasting a fully matured consumer society and technological prowess ..." (17) The economic prosperity Japan was experiencing at the time made this notion all the more appealing.
"The discourse on postmodernism popular in Japan at the time was unique in the way it deliberately confused and intermingled questions over what encompassed "postmodernism" and what encompassed "Japaneseness." (17)
According to Azuma, it was this climate of narcissism that facilitated the spread of otaku culture.
Azuma mentions narcissism at another point of the book as well, when describing the psychiatrist Saito Tamaki's psychoanalysis of battling beautiful girls. He says, "The girl images consumed in otaku culture basically have nothing to do with real women but are projections of the otaku's own obsession with his own phallus, i.e., a fetish object created by the projection of narcissism." (135)