The more balanced you are the larger the Strike-Zone (Hitting-Zone) becomes. Solid contact within the strike zone produces a heavier and more consistent shot. The better your balance, the more likely you'll hit a great shot.
The use of the body to start your swing and generate racquet head speed allows for less strain on the shoulder, arm, elbow and wrist. Because you are using the larger muscles as the basis for the swing of the racquet you are also more likely to produce a more consistent stroke, and will find it easier to add power to the stroke.
body rotation example video 1 forehand
body rotation example video 2 backhand
Tennis, like baseball and golf, is a "sideways sport". You make contact with the ball to the side of your body, not in front of you. Your grip will determine where within the strike zone is best for you to make contact.
To greatly enhance your play concentrate on good footwork and balance, start your swing with strong body rotation (not your hand), and contact the ball within your strike zone.