I have seen this reference in several places and I don't quite understand what it is and its significance. I am new to tube radios and keen to learn. Any simple explanation is appreciated. Regards, Angelo

First, to explain bias with a cathode resistor:
Take a typical audio amplifier stage, using for example a 6V6 beam tetrode. It requires negative 12.5V on the control grid to set the correct operating conditions. (The valve is designed to operate at a certain current where its gain is most linear). One way to provide this is of course to use a battery. Batteries have disadvantages, so another way to obtain the bias is to connect the valve cathode to earth via a resistor. Current flowing through the valve causes a voltage drop across the resistor, and by selecting the appropriate value of resistor, the voltage drop can be made the same as the required bias.
Basically, if the cathode of a valve is above earth by positive 12.5V, and the grid is earthed (via a high value resistor so as not to impede the incoming audio), that is the same as saying the grid is negative with respect to cathode by 12.5V.
If for some reason the valve current should increase (e.g high mains voltage, slightly gassy valve, etc.) the bias will automatically increase and therefore reduce the valve current to compensate. This system of bias is called "cathode" or "automatic" bias.
Now to the capacitor; it's there to prevent loss of audio gain.
To try and explain this simply, the cathode bias resistor voltage drop fluctuates with the plate current - that is after all the whole point of automatic bias. And of course, plate current fluctuates with the audio signal. It can be seen that as the bias fluctuates, then there's negative feedback which reduces gain of that stage. What we want is for the bias to fluctuate only with DC and not the AC signal.
Hence a bypass capacitor is connected across the cathode bias resistor. It appears as a short circuit to AC, and open circuit to DC.
So far as the cathode of the vale is concerned, it is effectively earthed for audio signals and no loss of gain can occur.

Some circuits do in fact have no cathode bypass capacitor, as a method of reducing stage gain for stability reasons, or to deliberately introduce negative feedback in the interests of sound quality.
The value of capacitor can also be chosen to give a particular frequency response for an audio stage, but that's getting a bit ahead of the question here.

Thankyou Cool386, that was a great explanation.

I wish to second the the thumbs up from Fendertweed,
it is a great explanation as it makes sense to a newbie
tubeie such as myself. Thanks Cool386 !