Suspensions are employed to deal with humps in road surface, in other words, enhancing ride comfort. When a car rides over a hump, the springs are compressed, store the energy thus provide shock absorption. The energy will be released quickly when the springs bounce back.
Dampers are employed to smooth and slow down the bounce motion, this is called "Damping". Without dampers, the car will bounce up and down severely and quickly, this is perceived as uncomfortable. Studies found that ride is perceived as comfortable by human when the bouncing frequency is 1 to 1.5 Hz. If it expeeds 2 Hz, most people feel the ride to be harsh. Therefore ride quality is mostly controlled by the selection of suitable springs and dampers.
Although we state here that suspension is employed to enhance ride comfort, by ironing out bumps and humps, this does give the benifit of better handling/grip.
If we have no suspension when wheel encounters bump, wheel will leave road, when wheel leaves road tyre has no contact with tarmac, no contact no grip, no grip no turn etc etc.
In order to achieve ride comfort, we create suspensions and let the wheels move with respect to the car body. Inevitably, this creates many many problems in handling. When the car is turning quickly into a bend, centrifugal force will roll the car body. Body roll leads to the weight transfer towards the outside wheels, it also changes the suspensions geometry which changes the camber angles of wheels. Change of camber accompanied with weight transfer results in unwanted understeer or oversteer. If brakes are applied in the bend, castor angles will also be changed, that may further deteriorated understeer / oversteer or even introduce torque steer.
1) Provide independent shock absorption to individual wheels. That means, when one wheel rides over a hump, the shock will not be transferred to other wheels.
2) Have adequate body roll. Excessive body roll leads to too much weight transfer thus influence the steering response. It is not comfortable too. Overly restricting body roll to a minimal may create uncomfortable feelings because of excessive g-forces. Moreover, body roll could provide information to the driver, telling him the state of cornering and whether the car has reached its limit.
3) Has a good geometry such that wheel cambers remain unchanged in all conditions of acceleration, braking, cornering, load and bumps.
In the perfect world a suspension system would be just hard enough to suppress body roll, and just soft enough to clamber over any bump we can find. Unfortunately the road surfaces (at least around here) are a bit more varied than that and suspension setting become a compromise between comfort and handling.