The fuzz on a tennis ball allows the ball to travel further without greatly increasing its speed, and it also allows for better control of the ball. When the tennis racket strikes the ball, it is able to slightly grip the ball's fuzz to better manipulate and control its flight.
The fuzz on a tennis ball also increases the ball's durability over other plain rubber-type balls. The fuzz also helps control the flight of the tennis ball. Its slight resistance helps slow the ball down when traveling at fast speeds and increase its speed slightly when traveling at slow speeds.