When we talk about using the ground in the golf swing, we're referring to the golfer's ability to use vertical and horizontal ground reaction forces to produce rotational force, or torque.
This is a great drill to help achieve greater clubhead speed for longer shots. All you need is a tennis ball cut in half and placed under the ball of the left foot, as shown in the pictures.
To produce speed, the golfer must transfer force to the club (since acceleration is necessary to produce speed, force is necessary to produce acceleration).
This force is transferred through what is often referred to as the "kinetic chain", meaning it is transferred through the linked movement of different body segments. The movements are initiated in a specific sequence, beginning with the segments furthest away from the club, the feet and legs, and gradually progressing through the hips, trunk, shoulders, and arms before ending with the segments closest to the club, the wrists and hands. Due to the rotational movement of the golf swing, the ability to produce torque at the feet (pressing down into the tennis ball to start the downswing) for subsequent transfer is essential for the golfer, with greater torque generally resulting in greater clubhead speed.
Naturally, the force must come from somewhere, which is where ground reaction forces become important. To produce the necessary force for the swing the golfer needs to work against an external resistance, so the primary means of generating large forces at the feet is by pressing against the ground.
If there is no external resistance, the golfer is unable to add force to the system and consequently there is no total change in movement. Imagine performing a golf swing on ice (or in the air). With no resistance at the feet, rotating the upper body toward the trail foot in the backswing would result in the lower body rotating toward the lead foot, so that there is no total change in movement (the two movements in opposite directions cancel each other out).
Similarly, rotating the upper body toward the lead foot in the downswing would result in the lower body rotating toward the trail foot. In short, without the ability to produce torque at the feet the golfer would lose control over both the magnitude and the direction of hip rotation as well as its relation to shoulder rotation, which are instrumental to the swing.