Courtesy of AnnaV :
By heating cord your book probably means the wire or flex which conducts electricity from the power supply to the heater. This is made of copper andbecause it has very little resistance to current, compared with the resistance of the heating element, which is very high. The electrical power dissipated in a resistance $r$ when current $I$ flows through it is $I^2r$. The same current flows through the wire and the element, but the resistance of the element is very much larger. Very little electrical energy is dissipated in the wire so it does not get hot and does not glow - unlike the heating element.