A golf swing is much like a slap shot in hockey. A good golf swing is vital in the game of golf.
A golf swing is almost all rotational energy. A higher velocity means more rotational energy. The more energy in your swing leads to more energy transferred to the golf ball. The more energy you can transfer to ball the farther it will go.
The angle at which the club hits the ball is also important. You want the face of the club to be completely flat when it comes into contact with the ball. If it makes contact at an angle, it will cause the ball to spin. The spin of the ball causes friction with the air resistance causing the ball to bend, and the ball will slice. This is much like how soccer players are able to bend the balls on shots and free kicks. The club is like the players leg, and the soccer ball is the golf ball.