The Children are minions doing the bidding of the New Gods.
In the novel, the "children" are the unseen underlings of the Technical Boy.
They appear only in Chapter Two : they are the ones that kidnap Shadow by putting on his mouth a wet cloth with chemical products. When Shadow is interrogated by the Technical Boy in his limo, two of the "children" are present, one on each side of Shadow. Shadow can't see them due to the straps that bind him. The Technical Boy orders one of them to hit Shadow after the later mocked him, and they do so. He also talks to the driver of the limo, that may be another one of the "children".
Outside of this apparition, the "children" are only mentionned in Chapter Fourteen, by the Technical Boy. He mentions that the "children" can't "operate" in the Center of America due to it being a "dead zone" (as in, a location without any WiFi or Internet connection). This clearly indicates the inhuman and technological nature of the "children". In a similar way, during the first Interlude, not only are the "children" nowhere to be seen, but the limo of the Technical Boy is also shown to be self-driving.
Television series Edit
In the television series the Children play a larger role than in the novel. Faceless men able to manifest out of nothing as virtual constructs and to multiply at will, they seem to be the embodiment of the "faceless goons" trope, the archetype of the generic and disposable minions and servants only here to highlight or protect a more important character, a concept found in numerous movies and video games.
Their first appearance is in The Bone Orchard, where they help Technical Boy interrogating Shadow. Dressed up as the Droogs, a group of violent criminals from the movie "Clockwork Orange", they beat up Shadow on the orders of the Technical Boy and later try to lynch him. They are however all slaughtered by Laura Moon/Series.
Their second and final appearance is in Come to Jesus. One of the Children is seen accompanying Media to Easter's party. Since Media took the shape of Hannah Brown, the character played by Judy Garland in the movie "Easter Parade", the Child appears as Don Hewes, the deuteragonist of the movie played by Fred Astair. When Media threatens Easter later in the episode, the Child multiplies into a whole group of Children that threatens the Old Goddess by using their body gestures, in a way similar to background dancers in a musical movie. This episode also reveals that the Children can be used as "portals", "doors" or "windows" by the other New Gods, since Technical Boy appears out of the division of two Children, and Mr. World takes possession of one of the Children to speak through him, his face appearing instead of the Child's blank head. The Children were sacrificed as a whole by Mr. Wednesday to Easter, killed all at once by a lightning bolt and their lives offered to the goddess of spring.
Due to them not appearing in season 2, their death is presumed to be final. It also seems that any damage inflicted on one of the Children when possessed are also inflicted at a lesser degree on the New God currently possessing the Child: Mr. World, in House on the Rock, mentions that Mr. Wednesday could have "killed" him.