Simply put, dampening is how much travel the shock does when compressing and rebounding. Think of it is as how stiff the shock will be. With the Koni Yello shocks or the Tokico Illumina shocks you can adjust the level of "stiffness" aka dampening by turning a dial/screw that is mounted on top of the shock. I believe a stiffer setup will allow the tires to be in contact with the road more while going over bumps and certainly allow you to corner harder.
So if you are going to get coilovers, you can get ones that allow the ride hight to be adjusted as well as the stiffness...