This component falls into the category of the throttle-organs. What is meant, is not the simple throttle, but the expansion-valve. It is so called, because it regulates the expansion in the evaporator in such a way, that as little as possible liquid refrigerant is left over. It is also a matter of protecting the compressor.
Basically, we have a thin tube carrying liquid coolant to the evaporator and a thick tube carrying gaseous coolant from the evaporator to the compressor of the expansion-valve. The thin tube, ergo the inflow to the evaporator, is regulated.
First of all, try to imagine a simple spring-loaded valve, where a membrane works against the spring. What it's trying to do, is to open the valve wider. Thereby, it is helped by the pressure from a temperature sensor found in the thick tube. If the temperature rises and wth it the the pressure compared with the the evaporation pressure, then more coolant flows through the evaporator.
This then, is the temperature regulated expansion-valve. It is quite clear, that in this case, we're dealing with a regulation, because when more coolant flows through the exaporator, it can no longer heat up as strongly. Indeed, the temperature should be determined directly at the output from the evaporator.
As mentioned above, the membrane receives the force it needs, to try and open the valve wider, supported by the pressure of the temperature sensor and as a reaction against the pressure in the evaporating coolant. This is described as the internal pressure equalisation. If in addition, one takes the pressure from the output of the evaporator, we then have an external pressure equalisation.
This type of expansion-valve is somewhat more complex, but can manage with less overheating. Overheating means, the additional heat above the boiling point of the coolant. It is rather unnecessary for the heat transportation of the air-conditioner, thus, lowers it's efficiency. In larger systems, more expansion-valves with external pressure equalisation are installed. 11/13