I once owned a monitor with a permanently printed windows 3.1 desktop on it. It was still usable, but when turned off, you could see the damage well enough to read the windows menus on the normally dark screen. This monitor was a 13 inch black and white CRT that was probably manufactured at the very beginning of the 1990s.
CRT are just electron guns aiming at a phosphorous surface. When an electron hits that surface, an electron belonging to a phosphor atom gets excited and when it drops back to its normal energy level, it emits a photon of a certain frequency. Repeat the same process many times per second and in an ordered fashion and you will be able to display graphics. When the image on a CRT is left standing still for a long duration, the repetitive hit of electrons on the inside phosphorous layer degrade it, making it more transparent where the image is the most bright. Screen savers were invented to prevent this phenomenon; to save screens that were left on.
With LCDs, there is no such phenomenon; using a screen saver is dumb and only wastes power. Instead, set your computer to put it in standby after a few minutes of inactivity, or discipline youself and turn it off using the power button, which is better because the screen uses less standby power that way.