The picture you observe when you are shaking a pen in front of a computer or TV screen is a result of the averaging action of the eye.
When you are shaking a pen in front of a wall illuminated by natural light, you see a continuous blur. Both the wall and the pen contribute to the brightness of the blur. The brighter the wall in comparison with the pen, the greater its relative contribution - so you'll see more of the wall than the pen. If the pen has a bright band in the middle, the blur will have a corresponding bright band as well, i.e., you'll see more of the pen there.
When you are shaking a pen in front of a TV screen, what you see, similarly, depends on the brightness of the part of the screen behind the pen, the background.
If the background is black, you'll see a lot of the pen in the blur. If the background is bright, you'll see mostly the background itself, except at the moments, when the screen goes dark as part of the refresh cycle and, correspondingly, at those moments, you'll see mostly the pen and, overall, a darker image due to a lower average brightness.
In summary, the blur is caused by the inertia (averaging action) of the eye, but the discrete nature of the image of the shaking pen in front of a TV screen is due to the refresh cycle and would be apparent even if the eye had no inertia.