Let me try and explain:
The higher resolution your graphics card has to render an image of a 3D scene, the more "GPU power" you need. Let's say that you have told the computer (using settings) to render the image at 1920x1080 pixels. Now if you have a 4K monitor 3840x2160, and you send the 1920x1080 image to the monitor, there are two options.
Either the monitor can show the image 1:1 pixelwise, meaning that you only have information for 1/4 the pixels of the 4K display, which has double the amount of pixels in both height and width. That typically shows up as the image in the middle of the display, with a black border around it.
The other option is to go "fullscreen". But... you cant. You have no image information for 3/4 of the pixels. The solution for the monitor is to "rescale" the image. One way of doing that is to make any pixel four times larger, so that it fills 2x2 pixels on the display. The result of that is similar to moving your head (eyes) closer to the display. You start to notice lack of resolution (visual pixels) and lack of details (image information).
A better option could be to smear two pixels, next to each other, sort of blurring them together, by taking the average of the two pixels, to create new "in-between" pixels. Now you won't see large pixels, but you will still lack the details, because they simply aren't there. Your monitor does that, when you view any image that is not at the displays native resolution. It looks "blurry".
Next up, you can sharpen the resulting image (the blurry one after the rescale). You do that by increasing the contrast locally (called "ringing"), where the contrast is low, and not in the rest of the image. Say you have a grey circle on a grey background. If you increase the contrast, only at the edge of the circle, then your eyes will perceive it as sharpness.
especially at a distance
This method can be combined into one, so that the image is upscaled and sharpened, in one move, like the "Lanczos" algorithm, but it takes calculation, meaning it takes time. There are way more complicated ways of upscaling and adding "sharpness" and "details", like using AI. They demand more calculation than your monitor can do, and are done in CPU or GPU.
I do not know the exact algorithm used for FSR, but it's good. I run a 4K+ VR headset, and I can't get resolution enough. I have my eyes less than an inch from the display, so I see the circle above in the large version. However, when I render at lower resolution ~3K and use rescale via FSR I get the best result I've had in Odyssey so far. Decent upscaling, decent sharpness without artifacts and better fps because the GPU has less pixels to render (time consuming). The FSR upscaling is much faster than the 3D rendering.
All that being said, it's "cheating". The first thing to do is to optimize 3D rendering, but that's a whole different story, for some other day
