Suppose a person is measuring the length of a rod with a scale/ruler and the eye is at angle with the marking of the scale. To the observer, the marking on the scale coinciding with the end of the rod will be different depending on the position of the eye. Hence, there will be an error in the measurement of the length. This error is known as parallax error.
Parallax error is introduced due to erroneous way of measuring (human error) and is not introduced by the measuring device. In order to avoid this error, one must always make measurements with their eye perpendicularly over the marking.
Another way of removing this error would be to use digital instruments. For example, using digital calipers instead of vernier calipers and multimeters instead of voltmeters and ammeters.
Hence, digital measuring device has zero parallax error.