The coach's box is a term used in numerous sports. In baseball, it is the space where the first base coach and third base coach stands. One quirk in baseball, as stated by the official mlb.com rules 4.05 A view of the playing field at Busch Memorial Stadium, St. ... In baseball, a number of coaches assist in the smooth functioning of a team. ...

(a) The offensive team shall station two base coaches on the field during its term at bat, one near first base and one near third base. (b) Base coaches shall be limited to two in number and shall (1) be in team uniform, and (2) remain within the coach’s box at all times. PENALTY: The offending base coach shall be removed from the game, and shall leave the playing field. Rule 4.05 Comment: It has been common practice for many years for some coaches to put one foot outside the coach’s box or stand astride or otherwise be slightly outside the coaching box lines. The coach shall not be considered out of the box unless the opposing manager complains, and then, the umpire shall strictly enforce the rule and require all coaches (on both teams) to remain in the coach’s box at all times. It is also common practice for a coach who has a play at his base to leave the coach’s box to signal the player to slide, advance or return to a base. This may be allowed if the coach does not interfere with the play in any manner.^[1]

In basketball, it's a line that represents how far a coach may come towards centercourt. In soccer, the coach's box is simply a term for the typical area that the coach or manager is standing. Basketball is a team sport in which two teams of five active players each try to score points against one another by throwing a ball through a 10-foot high hoop (the basket) under organized rules. ... Football is a ball game played between two teams of eleven players, each attempting to win by scoring more goals than their opponent. ...

References

1. ^ http://mlb.mlb.com/mlb/official_info/official_rules/start_end_4.jsp