These are also called "blow off valves". They are a mechanical valve which sits inside the pipework between the turbo and the throttle plenum. When the car is being driven under turbo boost pressure (which can be in the region of 14psi positive pressure) and the driver takes their foot off the throttle, the pipework suddenly has a lot of pressure with nowhere to go.
A standard dump valve (DV) has a vaccum feed to it (normally a small bore pipe) which in the S14a comes from under the throttle plenum. This is used to open a diaphragm within the DV and the boost pressure is vented back into the air intake pipe, just after the air fuel meter (AFM). This type of DV is called a recirculating type as the pressurised air is kept within the pipework. The advantage of this system is that the AFM can measure the air that has flowed into the pipework and the ECU can then add fuel in the correct ratio.
The standard dump valve that comes with the S14a can be seen in the picture above (thanks to Adam from the SXOC for the picture). The vacuum feed is the top pipe, pressure enters the valve through the bottom pipe and is "dumped" through the middle pipe.
Nissan designed the valve with a small hole between the two internal chambers. This is generally accepted to aid smooth throttle response, especially when coming off high boost levels. However, it also is a small "leak" that limits the maximum amount of boost you can run and also reduces the loudness of the dumping sound. A common modification therfore is to block up the small hole inside the valve with a small grub screw (tap the hole to M5).
It is very popular to replace the standard DV with an aftermarket version and often to vent the exhaust from the valve to the atmosphere - "vent to air". This give a much louder venting noise (which some people like a lot). The disadvantage is that this vented pressure is not then measured by the AFM and unburnt fuel is allowed into the exhaust where it poisons the catalyst as well as creating flames from the tail pipe.
The other alternative is to remove the DV entirely. In this scenario, the pressure is pushed back through the compressor wheel of the turbo and makes a "cooing" noise as the compressor wheel stalls slightly - often therefore called compressor stall. This has two disadvantages - it slows down the compressor wheel and therefore increases turbo lag and it also puts extra stress on the turbo bearings.