A Vacuum Solenoid Valve (VSV) is an electrically operated valve. An electrical signal from the ECU in the case of the EGR valve, or a push button in the case of the 4X4 transfer, either opens or closes the VSV which supplies or removes engine vacuum at the device being controlled. If the VSV goes bad, it no longer opens or closes the vacuum valve and the device (EGR valve, 4X4 transfer, etc) not longer works.
The ECU is connected to temperature sensors, oxygen sensors, speed sensors, throttle position sensor, etc. The ECU measures input from these sensors and then controls devices such as the fuel pressure regulator, egr valve, fuel injectors, etc to make the engine perform per it's design specifications. So if a subsystem such as the EGR valve is not working, then you have to investigate all the components of the EGR subsystem to find out which one has failed. There are sensors, wires, vacuum lines, the ECU and the EGR valve itself. In my case, I was not getting any engine error codes, but discovered that the tube connected to the EGR valve that goes into the engine was nearly plugged with carbon.
Additionally, any vacuum actuated device will have a rubber diaphragm internally that heat and time make brittle, and it's just a matter of time till they crack and fail. This includes the EGR valve, the EGR modulator (right next to the EGR valve), the fuel pressure regulator, the fuel pulsation dampener, etc. You can replace them as maintenance items before they fail, or wait until they fail and hope it doesn't happen too far out in the bush.