Overpressure relief valves are pretty much standard on today's BCDs. You can identify them as the vent-like areas, either on the shoulder and / or bottom rear of the jacket. Often they have a ball-and-string assembly attached called a "dump valve." Pulling on this will release air from the BCD through the valve. This allows the diver to vent air easily from almost any orientation underwater, without awkwardly holding their inflator hose toward the surface.
As their name implies, the primary purpose of overpressure relief valves is to prevent the accidental over-inflation of BCDs. BCDs contain what are called bladders, or basically, air bags. These air bags have a finite amount of air they can hold, and exceeding this amount, either by over-filling it or by ascending to a depth that increases the air's volume enough, would ordinarily cause it to rupture.
The trick is to put a hole in the bladder, but a hole that only leaks air when there's too much of it. This is accomplished by holding a plug in place over the hole with a spring. This plug effectively corks up the hole. The spring has to be perfectly strong enough to hold the plug in place while air enters the BCD, but weak enough so that the plug pushes out, releasing air, when the pressure inside the bladder gets too high.
BCDs have some maximum pressure they can withstand. This is easy enough for the manufacturer to find out. Just fill the BCD until it explodes. The pressure right before it pops is the maximum pressure, although they'll lower this a bit for a built-in tolerance.
With this maximum pressure p~max~, we can figure out the strength, or stiffness the spring should be. We do this using Hooke's law, which states that the force of the spring is equal to the deformation of the spring times a spring constant (the stiffness of the spring), or,
F = -k x,
where k is the spring constant that we want to find. We know what force is keeping the plug in place, it is the maximum pressure times the area of the part of the plug that feels the BCD's air pressure (pressure is force per unit area), or p~max~A. The spring is also be deformed slightly to hold the plug firmly in place. How much the spring is deformed gives us x, which tells us the force exerted by the spring on the plug. With that number we can rearrange and compute the spring constant as
k = -p~max~A / x.^1^
If the pressure increases, the spring won't be strong enough to hold the plug in, and the BCD will release air. You can also manually override the valve by pulling the plug yourself, which is what you are doing when you pull the cord.
Like most parts on a BCD, the overpressure valve is an incredibly simple device. The simplicity of this device helps make BCD inspections a fairly easy process, especially when compared to overhauling a regulator.
1. We are ignoring the mass of the spring and the plug.
: http://thedivingblog.com/uploads/2010/03/overpressure_valve.jpg : http://thedivingblog.com/uploads/2010/03/overpressure_relief_valve.png