A Faraday Shield (or cage or screen, etc.) is simply an "envelope" around the protected circuit. It may be solid metal, or it may be woven or perforated, etc. But in any case the purpose is to simply block outside interference from reaching the protected circuit by "intercepting" the interference and conducting it away to ground/earth so that it can't reach any sensitive part of the circuit.
Examples of Faraday Shields include your microwave oven (the Faraday Shield keeps the microwaves INSIDE the box so they don't escape). Many devices we use every day have metallic (or conductive) shields around them including cables, connectors, even storage devices like tubes that ICs are shipped in, or those metalic-looking plastic bags that protect against static damage. Even your car is a "Faraday Cage" against a lightning strike (and also somewhat reduces the efficiency of your cell phone unless close to a window, etc.)
http://en.wikipedia.org/wiki/Faraday_cageInside your resistor substitution box, you might find one of several different materials. If the box is metal, then it forms the Faraday Shield intrinsically. If it is plastic, then there may be sheets of metal inside, or the inside may be painted/coated with a conductive substance. I sometimes glue common aluminum foil inside a plastic case when I need a Faraday Shield.