Temperature humidity meters use electrical changes to measure humidity.
Both temperature and humidity affect the electrical resistance and/or capacitance of a circuit. Electrical resistance is to do with how easily a current can pass through a conductive material and capacitance is to do with how much charge a capacitor can store.
This knowledge has been used to develop thermometers and other similar devices, like temperature and humidity meters.
Although the electrical changes are minute, they can be measured to work out reasonably accurate temperature and humidity readings.
There is an electrode in the sensor on a temperature and humidity meter, which measures the electrical resistance or capacitance and then sends the signal through the circuitry where it is altered in to a temperature or humidity reading.