They have great resistance at low temperatures but when they warm up their resistance decreases rapidly. Current can then flow through them. This makes them ideal as one of the components for a temperature sensor.
(Image: Thermistor in a Circuit)
When the thermistor is warmed up by the hair drier its resistance drops, this will take a few seconds. As its resistance drops current begins to flow from positive 9 volts to negative 0 volts. Current flows into the base of the transistors allowing the LED to light.