A good example to use. If you look through a tube, something like a paper towel holder and look at an item in the center of the tube. If you turn the tube slightly you can still see the item clearly. However, the center of the tube is not on the item any longer. So if the pellet were to go to the center of the tube it will not hit the item now.
A real world experience: When I first started I had a cheap scope with parallax errors and it almost cause me to quit. I began shooting from a rest on a table. When I shot from it I had perfect sight alignment so I was able to consistently hit targets with no problem. When I started using a bi pod, my alignment changed so my pellets were hitting a different POI. The groups were still small so I knew the gun was shooting straight but the groups moved to a different location. I would spend time chasing the zero and get back on target shooting off a bi-pod. When I shot off the table again, you guessed it, the POI was different. Once I figured out the problem (by asking other forum members) and learned how to check for and correct parallax errors it was no longer an issue.