Off-side or on-side is derived from how the ball is delivered into the batsman. If it is away from the batsman, it is off-side and that is the region where ball can be hit/played. If it is directed into the batsman, it is on(-to) him and it can be hit/played in that region only. Ball down the legside is not termed 'off' as batsman is not obliged to touch/hit it ('blind spot').
