There is a pretty good discussion of parallax in sights at:
Basically, parallax comes into play when the shooter does not keep his eye in the exact same position relative to the scope from shot to shot. This is easily seen if the scope is put in a fixed position and the reticle put on a fixed point. If the person lookiing throught the scope moves his head from side to side, the reticle appears to move across the field of view.
Parallax is due to the relative position of the reticle and the lenses inside the scope; it can be reduced or eliminated for a given range, and more expensive scopes have adjustments to do that. But manufacturers of less expensive scopes design a scope based on an assumption of what it will be used for. For example, a four power scope generally used for deer hunting, will usually be parallax free at 100 yards.
But other factors can cause the proplem to OP mentions. Adjusting scope power means moving or turning a lens or lenses. If the lens is not nearly perfect, it can introduce the kind of error the OP is experiencing, which has nothing to do with parallax.