A hard rubber plastic comb is made out of rubber so it doesn't conduct electricity. This means that it is an insulator. Unlike a conductor (a metal comb), an insulator keeps the electrons at the place of where it was rubbed instead of equally distributing them around the surface of the comb.
In a metal comb, the charges within the comb move around while in the rubber comb they can't move around because in an insulator, it doesn't allow the movement of charges.