Basically the answer is straightforward. and it has to do with pixel count and density. your display can manage 1920x1080 that means that it has 1920 Pixel rows on the horizontal and 1080 on the vertical. When you play a 720p game the game is configured to run at a resolution of 1280 on the horizontal and 720 on the vertical. Instead of playing the game in a small box in the middle of your screen most displays will make the image fit the display. This is known as upscaling.
But the problem with upscaling is that irrespective of the resolution of the display if you are playing a 720p game there is only ever 1280 horizontal rows and 720 Vertical rows of visual pixel data. This means that images look blockier, the sharpness is shot and...