The catcher's box is an area of the playing field located behind home plate in which the catcher must position himself to await a pitch. If a catcher is outside his box when a pitch is thrown, it is a balk. In practice, the box is rectangular and delimited by a chalk outline, like the two batter's boxes. Its configuration is specified in diagrams accompanying chapters 1.04 to 1.06 of the official rules.
The creation of the box dates back to the time catchers had very little protective gear and usually stood quite a ways behind home plate to await the pitch, especially when there were no runners on base, in order to catch the pitch after it had slowed down considerably. To prevent this tactic, the box was created. This primary reason is no longer a factor, as in the modern game, there would be no advantage to having the catcher positioned far from the plate, as it would only make the pitcher's job harder, by depriving him of a good target.
The only other instance in which the box is relevant is when an intentional walk or pitch-out is called. The catcher must be careful not to step outside his box before the pitch is delivered, lest he cause a balk. This is very rare however, and with the introduction of the automatic intentional walk in 2017, even more so.