A screensaver is, in theory, a program to prevent a static image to burn onto a screen. This was could happen with CRT screens. What would happen is that when the same image is displayed for a long time, it would "burn" into the phosphor.
To prevent that, screensavers were invented. They blanked the screen if the computer hasn't been used for a while, and unblanked it when the user pressed a key or moved the mouse.
One day someone came up with the idea of putting an animation on the screen instead of just blanking it.
Turns out, this is evil. It makes the computer use more power. Screensavers cause pollution without having any benefit than a very minor amusement effect.
Also, amusingly, the more a screen is powered on, the shorter it lasts. Thus, screensaver animations actually do the opposite from saving screens.
To prevent that, modern desktop environments have controls to specify how long the screensaver animation works before the screen is turned off. That's an unnecessary bit of complexity.
If I had my way, screensaver animations would be removed from all operating systems. People running their computers off of solar power could add them, if they wanted, but everyone else would be better off without them.