DSR basically renders each frame in hardware at the highest possible resolution it will support, then scales the image down to a lower resolution when it's actually drawn on the display.
It's the ultimate quality setting because the final image is drawn with finest possible detail. It's also the ultimate performance killer because it forces your GPU to render at maximal resolution then run a downscaler to re-render at displayed resolution. It doesn't make much difference either way when the display resolution is the same as the maximum supported resolution.
Most people leave it turned off, I think, unless they want to show off ultra quality screen captures and such. While the detail level is a little superior it is very costly on raw fps and makes the GPU run hot 100% of the time.
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