This post is based on a submission by reader Matthew Garland.
According to Lee Carol, co-author of "The Indigo Children", the term was never supposed to denote anything paranormal. Rather, Nancy Ann Tappe, who coined the term, had synesthesia and associated these children with the color indigo.
Nonetheless, there is definitely an underlying argument that is completely unsubstantiated: that these children "represent a higher state of human evolution". Of course, if we take evolutionary psychology to its extreme, the children do in fact represent a higher state of human evolution (just not that much higher; probably not what the indigo folks mean).