This experiment requires that your computer (or your TV) be in a very dark room. We're talking inky, here. Really dark. Stub your toe dark.
Your computer draws a picture on the screen by using an electron beam to energize phosphors on the inside of the glass; these then glow, giving off the light that you see. That's why you can use your computer (or watch TV; the screens work the same way) with the lights off.
There's another word that is related to phosphors: phosphorescence. Something that is phosphorescent will keep glowing, even after the source that energizes it is removed. (For a little while.) Will your computer screen do this? You betcha!
Make the room really dark, and turn off your monitor. It will still keep glowing for a while; can you see it?
Another test: put a picture on the screen that is bright some places, and dark others (like the little picture below!) Leave it on for a few minutes. Now turn your monitor off. The bright places will still glow, and the dark places (which have not been energized) will not.
The ghost of the Little Shop of Physics remains!
The same thing happens with TV sets, by the way. Try it and see!