Dampers counteract the springs' natural compressing and decompressing by resisting those forces. Dampers do this via hydraulic fluids being pushed through small valves inside the damper while the damper is in motion. A higher damper value equates to greater resistance.

A wheel's maximum grip level will be achieved when the spring is fully compressed. This is when that wheel has maximum weight being transfered through the suspension, tire, and to the track. In a generic sense that weight equals grip. How quickly or slowly that spring is allowed to fully compress is the job of the damper. Springs may dictate HOW MUCH weight is transferred, dampers dictate HOW and WHEN that weight is transferred.

The easiest way to begin to understand dampers is in a straight line, under braking or acceleration:

Under braking, much of the car's weight will shift from the rear of the car to the front. The front springs will compress while the rear springs will decompress (or rebound). The dampers do the same and will compress (front) and decompress (rear). The faster the front springs are allowed to achieve their most-compressed state, the faster the front tires will have maximum grip for that all important braking. A softer compression setting will give the least amount of resistance to the spring compressing, allowing weight to transfer very quickly once the brakes are applied. The rear damper compression setting will have no effect on what happens here, but the rebound will. A greater rebound setting will resist against the rear springs decompressing. If the spring is not allowed to rebound quickly, the rear tires will be somewhat lifted off the ground (exaggerated of course). Softer rebound settings in the rear will allow the rear tires to stay connected with the road and offer more rear-grip during that weight transfer to the front.

Under straight-line acceleration the complete opposite is happening, with the rear dampers compressing and the front dampers decompressing. Surely you will want maximum grip on the rear tires under acceleration, but the front tires may need grip adjustments to prevent understeer oversteer. You can adjust this condition by adjusting how the rear suspension compresses or how the front suspension rebounds.

The same philosophy can be applied laterally (side to side) as well. Long sweeping corners that do not involve large braking or accelerating will shift weight to the left and right of the car. How fast you allow that weight to transfer is up to you and can be adjusted via the left and right dampers, but keep in mind how that will also effect your front to rear damping.

If your car is equipped with fast-damping adjustments, everything above still applies but only when the suspension is in "fast motion". An example of your suspension moving in fast-motion is when you are hopping over curbing, something I like to call "curb smacking". This is when you are shocking the suspension into movement in a very short time frame. Hitting a curb at speed (like you might at Monza, or the final chicane at Magny-Cours) is forcing your suspension to compress or rebound in a much shorter time frame than normal weight transitions. This is where fast-damping comes into the mix.
