I guess this represents an advanced level layperson question. First of all, a curveball is a pitch thrown in baseball whereby a pitcher grips the ball on its seams then breaks his wrist when throwing the pitch in order to create spin on the ball. This can be confusing to a batter, as the spin is often difficult to detect. The ball curves as it reaches home plate, making it more difficult to hit than a pitch thrown without spin.
The pitch is called “the deuce,” because a catcher will use two fingers (one is used to indicate a fastball) to tell a pitcher to throw a curve ball. A catcher gives the signals near his or her crotch (using his or her legs to shield the signal) so as to prevent the opposing team from seeing the signal.