You have the pump on your compressor and then you have the tank that stores the pressurized air. In the beginning, the tank is filled with regular air and during operation, the pump fills this tank with pressurized air. The tank has a set limit as to who much pressure it can handle, and if that limit should be crossed, there is no doubt that physics will take over and the tank will explode.
The pressure switch is there to prevent that from happening. The pressure switch, uses a pressure gauge to keep track of the pressure that is building up inside the storage tank. When a set pressure is sensed inside the tank, the pressure switch takes over and turns off the pump. That is all it does but it is a very important task. The alternative is to imagine scenario where the storage tank explodes, causing all sorts of danger.
The pressure switch is an important component of any air compression system, especially from a safety perspective. From what we know about switches, there are two kinds of switches that you will find. You have switches that come with digital pressure readouts and then you have the analog pressure indicators. Both eventually end up turning off the pump on time, but as is the case with anything digital, the digital readouts is far more accurate.
One benefit of opting to go with switches with digital gauges is that the better accuracy leads to more energy savings. With digital information the switches can become active at the right level. Over time, analog indicators tend to lose their accuracy, which does not happen with digital meters. Of course, this extra comes at an extra price. It is not that analog readouts are a deal breaker, rather, digital meter based switches are simply preferable.