This is a phrase used in baseball to describe a hit made from one side of the plate which travels to the opposite side of the field. For example, if a right handed batter hit the ball into left field, this would be considered an opposite field hit. From the batter's perspective, they are hitting it to the "right side" of the field, known as left field because the defensive perspective is used to assign position names in baseball. It is harder to hit the ball to the other side of the field because it requires that the bat contact the ball earlier in its flight path, which translates to less than full power in the swing.
Sometimes a fan or sports broadcaster will refer to the batter as "pushing" the ball into the opposite field. This serves as the opposite of "pulling" the ball, which is when a player hits the ball to the same side of the field they bat from. A player who is capable of hitting to the opposite field consistently is valuable to their team because of this ability. If the defense knows a player up to bat is capable of hitting the ball into the opposite field, they may shift their positions accordingly to adjust.