This baseball term refers to a play in which a runner is able to advance a base due to a choice made by the defense. It will most often be an attempt to get another player out at a different base, or indifference to the player advancing a base. It is called a fielder's choice because the defender, or fielder, has an option of where to throw the ball to get an out or not let a runner advance.
The most common situation for a fielder's choice involves a runner moving towards third base after a hit. Rather than get the batter out at first base, the defense makes the decision to throw to third and get the lead runner out. In this case, a "fielder's choice", or "FC", would be marked on the scorecard to denote that the runner reached first base due to a decision on the part of the defense.
There is good baseball strategy behind a play where the defense lets a player advance or reach base. By allowing a player to advance, the defensive team can leave a base open. This means the pitcher now has the ability to walk the batter without advancing any more runners, and that if the ball is hit, the player who advanced is not guaranteed to do so. If the choice has been made to let a player reach base in order to get another player out, it is often to get out the lead runner (the runner who has advanced farthest on base). By doing this, the defense prevents a run and reduces the chances of another run being scored.