Compression
The blue knob - compression adjustments restrict how freely the fluid moves through the damper via ports and shims. The more restrictions, the more firm your shock will feel. Depending on the manufacturer, compressions adjustments will have a fully open or soft setting and a firm or even locked out setting plus additional settings in the middle for fine tuning to personal preference.
Air Pressure or Coil
Air pressure or metal coils work in tandem with the compression settings and are the main dictator of how the shock will ride in terms of sage, softness, and firmness.
Rebound
Rebound works in the same way of compression but with the opposite effect. After a shock is compressed it will rebound toward its beginning position. The rebound adjustment uses ports and shims to restrict the flow of oil in the damper to slow or speed up the rate of rebound.