Without compression damping your fork or rear shock would compress with only the resistance of your air spring and in essence will act like a pogo-stick. Adding compression damping makes it more difficult to compress your suspension and adds desirable control characteristics to your components. i.e. platform, g-out control, bottom out control, and lockout.
While most components utilize a simple overall compression control (CTD, RP, etc.) other components utilize both low-speed and hi-speed compression controls