Back in the old days of TV all the video in the US had to conform to the
NTSC standards. That standard included a vertical sweep of 525 lines,
which were interlaced so a single frame of video took two complete
sweeps, for a vertical resolution of 262.5. This is the equivalent of
262.5 rows of "Pixels" in today's terminology. Since the aspect ratio
was 3:4, that means the equivalent Horizontal rate was 350. Thus the
resolution in the good old days was about 350X262.5--pretty sad by
today's standards.

That explains why your computer display looked so bad if you managed to
get it pumped into your TV at all.

Now days the typical resolution of HD TV is 1920 X 1080. There are
other standards even higher.
http://en.wikipedia.org/wiki/File:Vector_Video_Standards2.svg

The modern display does not treat incoming video from your monitor any
differently than it does video from the built in digital tuner. If you
TV looks good displaying digital TV, it will look good displaying
Digital Video from your computer Video card.