Main focus: Increase strength and tone in the arm, shoulders, back, chest and midsection. Various types of push-up put more emphasis on different areas, e.g. hands together targets the Triceps.
Without CoolBoard: Push-ups done on the floor fix your hands and feet relative to each other, so the only work being done is in lifting your body weight.
With CoolBoard: Now your hands can move in all directions. Your body must control and minimise that movement so more muscles must do more work. Your core and many stabilising structures must constantly work to hold the CoolBoard steady while executing the push-up. Think gym ball training on steroids!