The basic system that is found on early cars consists of a pump that is driven by the motor and that creates about 170 bars of pressure. An accumulator then distributes the pressure around the hydraulic system. This obviously includes the suspension but on other models (notably the DS), it also includes the power steering, power brakes and a hydraulic clutch, all significant advances for its time. There are four suspension spheres (pictured below), each of them is hooked up to a suspension arm via a piston that moves up and down as the suspension arm does. The piston pushes liquid into the sphere which contains compressed air and is separated from the liquid by a membrane. The whole lot of it swallows road imperfections effortlessly.
Cars equipped with this system will automatically lower very close to the ground when parked for a long time. This means that when you start them, you have to wait for them to rise up before you can drive them. This system eliminates the need for a conventional jack- if you get a flat tire, set the car to the highest level, put the jack under it and then set the car to a lower level.
Like everything it has its ups and downs (pun not intended.. or was it?) Since the system auto-adjusts the height of the car, you can tow your trailer or load up your trunk and the ground clearance will stay even. The comfort and the road handling are both outstanding. On the other hand, it's obviously a lot more maintenance intensive than a standard suspension system: the spheres can leak, the membrane inside the spheres can break and if the whole system goes haywire (i.e. the pump gives out), the car is undrivable.
It should be worth nothing that later cars such as the current C5 and C6 use a variation of this called Hydractive. While the basics are the same (pump/etc), it's an infinitely more complicated system that relies heavily on computers.
A 1983 GSA at the highest setting:
A 1973 DS at the lowest setting: