'Diagonal' damping is where things start getting a bit more complicated, and fun. Imagine what is happening to the right-front suspension of your simulated racecar as we go barreling into a left turn. As you lift off the throttle and apply brakes the weight of the car is being shifted from the rear of the car to the front. Added to this is a left-to-right shift as you begin to turn in to the corner. The right-front spring will compress under the weight transfer, and the shock will do the same. A low compression setting will allow that spring to compress quickly, giving that tire its full available share of grip very quickly. A higher compression setting will force the spring to compress more slowly, meaning the weight of the car will not transfer as quickly and maximum grip will still be available, just slightly later in the phase of the turn. The spring will fully compress no matter what the shocks compression setting is, but you can dictate WHEN and dictate the handling of the car during this phase of the corner. 

The opposite is happening to the left-rear of the car as it is losing weight both from braking and turning as that spring and shock is in a rebounding phase. How quickly that suspension is allowed to rebound dictates the grip for that wheel during this transition. If the shock is set to a low rebound setting then the spring will be allowed to easily decompress and maintain maximum grip. If set to a higher rebound, the spring will not be allowed to rebound as quickly and the grip will be reduced as the wheel is being pulled off the racing surface. You can imagine how this might affect the car during this corner-entry phase and how you can adjust it to suit your needs.

As the car approaches the middle of the corner, the springs are already at full compression and/or rebound, and the dampers would be as well. Dampers do not play a roll in the handling of the car once this has occurred, as dampers need to be in-travel (either compressing or rebounding). If the dampers are not in motion, they can not offer resistance.

As we pass the point in which the car is at a settled state in the middle of the turn, you begin to apply throttle for maximum exit speed. Applying the throttle will shift weight to the rear of the car, and as we ease out of the steering the weight will begin shifting back towards the left. As you apply throttle the right-rear shock begins to go into more compression, though would already be near its maximum compression. Since we cant make this spring and shock compress any further, actions can be taken from the diagonal corner (left-front). Altering how that spring deals with the weight shifting will increase or decrease overall front grip.

There are hundreds of variables in dampers, even though there are only four dampers on the car. Changing one will alter the other three as well. One adjustment to the right-front rebound will alter how the weight is shifted to the left-front wheel (Lateral weight transfer in quick succession turns like chicanes or long sweepers), the left-rear (diagonal weight transfer in corners while braking or accelerating), and the right-rear (Longitude weight transfer under braking and acceleration). You have to be aware how one change will affect the other aspects. As usual, any setup change is a compromise between a gain in one area and a loss in another.

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 then normal weight transitions. This is where fast-damping comes into the mix.
