The NME is a (rubbish) weekly music magazine/newspaper.
The NME Children are those who read it religiously, and once the NME says/does something, they do it too, to be cool.
One Prime Example: The NME says they like Pete Doherty, all the twelve year olds run around screaming they love him. Once the NME decides he broke up The Libertines, thus the NME don't like him anymore, the NME children rip up all their posters, cross out the hearts with his name written in them, and run aroud saying they hate him.
Normal person: What style of music would you say The Futureheads are?
NME Child: Art punk! The NME says so.
Normal person: Do you like The Killers?
NME Child: Of course I do! They're in the NME, like... Every week!