This is a baseball phrase used to describe the corner area of home plate opposite the current batter. When a batter comes up to bat, he/she stands on one side of home plate. Although the dimensions of home plate differ at different levels of competition, it is always a five sided rubber plate. It consists of a rectangle with a triangle attached to one long side. Home plate is positioned so the triangle's vertex is pointed at the catcher, which leaves the two short sides bordering the two batter's boxes. The outside corner is one of the corners on the short sides of the rectangle.
In order to get a strike on the batter, the pitcher wants the ball as far away from the batter while still going over the plate. This can be accomplished by pitching over the outside corner of the plate. If the ball is curving away from the batter, it may travel over the first corner. If the ball is curving in towards the batter, it may travel over the second corner. The term applies relative to the batter, and is never fixed. A pitcher may be skilled at pitching to the outside corner, but typically only one side or the other, depending on the handedness of the pitcher.