The idea behind suspension is to insulate and isolate the rider and chassis from the ground beneath. Any form of suspension will increase the comfort and traction available. The difference between good and bad suspension is feel, performance and efficiency. In a mountainbike frame this generally means a swingarm or linkage and a rear shock containing both the spring and the damper. The linkage controls where the suspension can move, the springs control how much force it takes to move and the damper controls how fast it can move.
Rear shocks can be either air, coil or elastomer sprung.
Air shocks are referred to as progressive or rising rate. This means their rates increase as they move through their stroke. Coil spring shocks are generally straight rate or linear, the rate doesn't increase as they move through their travel. There are exceptions though, all coil springs have a slight progressive nature and can be wound to become very progressive by using coils wound tighter in one section or tapered wire. The connecting linkage can be falling rate, straight rate, rising rate or a combination of the three.