Probably so the bat boy can retrieve it quickly to make way for the next batter.
The batter faces towards home plate, with their feet just further than shoulder width apart. If the batter is right handed, they will stand to the left of the plate, looking over their left shoulder at the pitcher. If the batter is left handed, they will stand to the right of the plate, looking of their right shoulder at the pitcher.
According to the H&K Sports Fields (commercial) website (refer to the link, below), the batter's box starts 6 inches from home plate, and measures 4 feet long by 6 feet wide, total (i.e., both the right and left sides combined).
As of the 2014 season, the Arizona Diamondbacks have 12 right handed batters.
As of the 2014 season, the Atlanta Braves have 10 right handed batters.
As of the 2014 season, the Baltimore Orioles have 10 right handed batters.
As of the 2014 season, the Cincinnati Reds have 10 right handed batters.
As of the 2014 season, the Cleveland Indians have 6 right handed batters.
As of the 2014 season, the Detroit Tigers have 11 right handed batters.
As of the 2014 season, the Oakland Athletics have 7 right handed batters.
As of the 2014 season, the Philadelphia Phillies have 8 right handed batters.
As of the 2014 season, the Pittsburgh Pirates have 11 right handed batters.
As of the 2014 season, the Seattle Mariners have 8 right handed batters.