In baseball, this term refers to a player who consistently attempts to hit the first ball pitched to him or her. A batter who attempts to hit the first ball pitched is singled out because this goes against the standard hitting strategy of waiting for a pitch. Batters will typically wait for a pitcher to throw at least one or two pitches before swinging. The idea is that a pitcher gets tired and less accurate with every pitch he or she throws. Furthermore, there is a famous saying in baseball, "You cannot strike out on one pitch." This is meant to teach batters that even if the first ball pitched to them is a strike, they should not swing at it because it will not get them out right away. A first-ball hitter attempts to turn the tables on pitchers who expect batters to wait, by swinging on that first pitch, which is often a strike.
First-ball hitters can be useful to a team because they are usually aggressive at the plate. This type of player will often try to hit lots of different types of pitches in different locations. This reduces the types of pitches a pitcher can throw, while also limiting his target area. By doing this, a batter makes a pitcher think and perhaps make a mistake and throw a bad pitch.
The extreme opposite of a first-ball hitter is a patient hitter, who will wait as long as possible before swinging. Rather than working to get a hit, this type of batter makes the pitcher work to get him/her out.