https://en.wikipedia.org/wiki/Screen_burn-in

Burn-in is almost not a problem with modern LCD screens.

CRTs had big burn-in problems.

Plasma screens (eg big TVs) had burn-in problems, at least prior to 2007.

OLEDs - a flat screen technology different from LCDs - can suffer burn-in. OLEDs are thinner and lighter than LCDs, and have greater contrast. OLEDs are common in phones and smartwatches (thinner, lighter) and some TVs (greater contrast). Also in some laptops (https://www.pcmag.com/picks/the-best-oled-laptops). OLEDs in general suffer color degradation over time, usually faster than LCDs go bad -- IIRC burn-in is this color degradation accelerated by use.

I have long hungered after some of the best looking OLED displays... but in general I am cheap and have LCDs. Some OLEDs

LCDs and OLEDs tend to suffer image persistence / retention problems - an old image remains slightly visible even though a new image is projected, but fades over time. "Over time" can be a while- Apple used to recommend mitigating image retention by displaying a white screen for the same amount of time as the image that you want to "un-persist" was displayed. So if you displayed it for several hours... ?

But LCDs and OLEDs can still suffer burn-in. Although much, much, less than CRTs.

At least, companies that sell anti-burn-in technologies say that LCD and OLED burn-in still occurs, Like https://www.agneovo.com/global/anti-burn-in-technology

And sites like https://www.makeuseof.com/tag/why-do-images-get-burned-into-lcd-and-plasma-displays-and-how-you-can-fix-it/ have pictures of burn-in on real flat-screen monitors.

Most people no longer worry about LCD and OLED burn-in, but if they do they do things like:

a) use screen savers (yup)

b) turn the screen off

c) display a blank (typically white) screen - which tends to equalize pixels

d) display noise / static patterns that change over time, B&W/gray or multicolor

e) for static images, regularly shift pixels.

Oh, did I mention that excessive heat can cause screen discoloration?

Anyway, several of these mitigation techniques may be automatically applied by your LCD or OLED or other display controller. Such automatic application is one reason why most of us worry much less about LCD and OLED burn-in.

For the most part, turning off your display - screen blanking as mentioned by others - is the most you need. Plus, it saves power, energy, battery life, ...

(Random noise patterns can help more, but are quite distracting if bright.)

DPG15.6 (also DPI 15.3) + KB, Sennheiser MB Pro 1 UC ML, BTD 800 dongle, Windows 10 Pro, MS Surface Book 3, Intel Core i7-1065G7 CPU @ 1.3/1.5GHz (4 cores, 8 logical, GPU=NVIDIA Quadro RTX 3000 with Max-Q Design.