Joe,
Unsprung weight is the stuf that
must move when a wheel hits a bump. The wheel, tire, upright, suspension arms, and maybe the brakes all contribute. The rest of the car - body, chassis, engine and payload are insulated from the road by the springs. A good thing.
One of the prime functions of the shock absorber (a terrible misnomer...) is to damp the motions of the unsprung weight. (Ever see a car with "bad shocks" going down the road with a wheel literally bouncing on the pavement?)
The more unsprung weight, the stiffer the required damper. The downside of a stiff damper is a poor ride, and possible loss of traction under bumpy conditions, plus there are transition issues - when the car turns into or out of a curve.
Sooo - the lower the unsprung weight, the better.