In road traffic usage, the side of a vehicle or draught animal away from the kerb (or "nearside"), as in "an offside turn, i.e. to the left in most countries, to the right in those countries inheriting British or pre-revolutionary Chinese practice, is always hazardous", or "the horse always pulls out like that because he used to be the offside member of a pair."
The term is useful because (unlike "right" and "left") its meaning is not absolute, but relative to local rules of the road.