(see pic above) that half of the field, as bisected by a line joining the wickets and extended both ways, which is in front of and away from the batter, i.e. the other half of the field (as opposed to his "leg" or "on" side).
In cricket, the off side is one half of the field. A cricket field is notionally divided into two halves, along a line running down the long axis of the pitch. In normal batting stance, the striking batsman stands side on to the bowler.