It will change between left and right as the bowler looks down the pitch, depending on whether the batsman is left or right handed but the on or leg side is always the side of the batsman's legs.
Some of the laws (particlularly LBW) are not the same for off side and leg side. It can cause a lot of problems when a batsman decides to bat the other way round as the bowler bowls - Pieterson did this against Sri Lanka.