Still none the wiser? ... well neither was I. Essentially it is a gas-filled glass envelope containing a very fine wire. The wire has a positive temperature coefficient and a very low thermal mass. These devices were used to stabilize valve (vacuum tube) heater currents against variations in supply voltage.
In another form, the Barretter is so sensitive that it responds at audio frequencies to changes in the RF power of an AM signal, thus demodulating it. According to the Wikipedia article, the principle is still used in some microwave detectors.