The best way to understand this is through an easy experiment. While in your parked car, take a look at the needle gauge in your car's speedometer. You will notice that when you look at it directly from front, it may show some speed. However, when viewed from other angles, the speed may appear different. The same is the case with clocks (with moving arms for hour and minutes). Parallax error is introduced when we do not look at an object directly along a normal. That is to say, when our line of sight is not perpendicular to the object, we obtain a false reading of the object.
Parallax error is commonly used by astronomers to determine the distance of stars by comparing the apparent shift with that of more distant stars. Since the more distant objects will have lesser parallax, the closer objects will be easier to measure against that background.
Hope this helps.