They have fuzz on them so the air the ball is traveling through can grip the ball to enhance the spin on the ball. ex. To move it farther (backspin) or to make it drop (topspin) or to make it curve to the side (sidespin). The fuzz also allows the ball to have better interaction with the surface, the air and the racquet. As the ball speed increases the fuzz filaments lay down on the ball and the fuzz drag declines.
The tennis ball cover is rough but not like sandpaper. Looking closely at the felt you can see that air flows through those raised fabric filaments - better known as fuzz. So the surface of a tennis ball is a "porous surface." It's more like dealing with the wind blowing through leaves on a tree and just as complicated. The fuzz filaments act like tiny cylinders each having their own drag component. In addition to the skin friction drag from the cover itself, drag is created from the airflow over these fuzz fibers interacting with all the other fibers behind it.
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Its more of a fuzz then hair. Its so the strings can grip the ball, giving it spin.
A tennis ball is fuzzy because the fuzz from the ball actually decreases the ball's speed while in flight. The fuzz also prevents the ball from bouncing too high.