your monitor is probably stretching the image to fit the screen. You don't say if you have a 16:9 or 4:3 display but I will assume it is 16:9
standard definition DTV is only broadcast at what can be called 480p for the sake of simplicity, also, it is a 4:3 ratio.
In other words, if you are only viewing a standard definition DTV feed on a 16:9 1080p capable display, the source image would be much smaller then the screen itself, it would fill most but not all of the vertical portion but would fill much less of the horizontal portion....you would have approx 1/6 or so of the screen on each side unused.
If this is not the case then your monitor is upscaling the source image which more than likely is the cause of the poor quality.
basically, the source image is a square and it's being squashed to fit into a rectangle....hopefully that explains what I am trying to say in a simple manner.