Flow switches as the name implies detect water movement - there are various types:
1- Differential Pressure Switches
2- Magnetic Reed Switches
3- Paddle Switches
4- Water Turbines
Differential Pressure Switches
These work by creating a different pressure either side of the diaphragm by way of introducing a Venturi into the pipework (a narrowing of the pipework which causes either a fluid or gas which is passing through the pipe to accelerate). At the narrowest point of the Venturi the pressure will drop and the differential pressure switch exploits this to create a positive and a negative pressure either side of a diaphragm. The movement of the diaphragm moves a push rod which results in the activation of a micro-switch which informs the PCB that there is water movement.
Magnetic Reed Switch
This is a simple switch - as water moves through the appliance the float lifts. At the end of the float is a magnet and the magnetic field closes the reed switch.
Again a simple mechanism - as water moves through the appliance a paddle is moved - the paddle is connected to a lever arm which opens or closes a switch.
The function of the turbine is as above to detect water movement however if this is used as a hot water flow switch it has the additional capability of quantifying the amount of water flowing through the appliance and therefore adjusting the burner output as the water flow rate increases or decreases to maintain a constant temperature.
These can also be used to detect water flow - there is a separate section on thermistors.
The faults normally associated with flow switches result from water quality issues - i.e. debris (magnetite or ferrous oxide) stuck on the components preventing movement and consequently their correct operation.