Tennis balls look green to some people's eyes, but they're actually bright yellow. Whatever color they appear to you, they're definitely fuzzy, though some are fuzzier than others. The felt material on the outside helps you maintain control of the high-speed ball as it impacts your racket, so it doesn't bounce away wildly. The aerodynamic drag of the fuzz also prevents the ball from flying through the air too rapidly, bouncing too high or reaching speeds that are too fast for players.
As the ball impacts the strings in your racket, the felt begins to fray, leaving the ball with a fuzzier look than when you began. You'll see a tennis player at the US Open and Wimbledon select less-fluffed balls before a serve in hopes of making the ball go fast enough that his opponent misses. By contrast, a competitor may opt to serve up a fluffy ball so play will be slightly slower if she knows her opponent consistently makes strong returns.