Blowing on the fingers dries them off a bit. It will result in a marginally better grip on the racquet. They can't really wipe their hands on their shirt or shorts - their clothing is damp with sweat. It's either that or call for a towel from one of the courtside assistants.
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Because bouncing the ball with such pressure causes a tingly sensation not to mention the nervousness of the game makes them sweaty so blowing on the hand makes it easier to grasp the ball and play the game