A video card can (not always) somewhat improve video quality.
However, video quality ultimately depends on how well the video was encoded. If it was encoded with low bitrate and / or poor settings then the result will be "bad video". The only real way to improve the video is to re-encode the video with higher bitrate and better encoding settings.
Other things that can affect the quality of the displayed video are:
1. The quality of TV or LCD monitor. Basically the display panel itself where it's LCD or plasma.
2. Quality of the connection. Meaning good quality cable and input and output ports.
3. Video card to a limited degree.
None of the above will improve the quality of a poorly encoded video.