A program which displays either a completely black image or a constantly changing image on a computer monitor to prevent a stationary image from "burning" into the phosphor of the screen. Screen savers usually start automatically after the computer has had no user input for a preset time. Some screen savers come with many different modules, each giving a different effect.
Approximately pre-1990, many cathode ray tubes, in TVs, computer monitors or elsewhere, were prone to "burn-in"; that is, if the same pattern (e.g., the WordPerfect status line; the Pong score readout; or a TV channel-number display) were shown at the same position on the screen for very long periods of time, the phosphor on the screen would "fatigue" and that part of the screen would seem greyed out, even when the CRT was off.
Eventually CRTs were developed which were resistant to burn-in (and which sometimes went into sleep mode after a period of inactivity); but in the meantime, solutions were developed: home video game systems of the era (e.g., Atari 2600s) would, when not being played, change the screen every few seconds, to avoid burn-in; and computer screen saver programs were developed.
The first screen savers were simple screen blankers - they just set the screen to all black, but, in the best case of creeping featurism ever recorded, these tiny (often under 1K long) programs grew without regard to efficiency or even basic usefulness. At first, small, innocuous display hacks (generally on an almost-black screen) were added. Later, more complex effects appeared, including animations (often with sound effects!) of arbitrary length and complexity.
Along the way, avoiding repetitive patterns and burn-in was completely forgotten and "screen savers" such as Pointcast were developed, which make no claim to save your monitor, but are simply bloated browsers for push media which self-start after the machine has been inactive for a few minutes.