The main purpose of a HDTV up-converter is to eliminate the analogue conversion by having the entire path from the DVD to the TV in digital such as using a DVI or HDMI cable. The up-conversion process also means that the player can work on TV's that cannot handle 480p or 480i, although most HDTV sets can perform the up-conversion.
If one connects a DVD player up to a HDTV display using a SVHS, RCA, component or SCART (in Europe) lead, the DVD player does a digital to analogue conversion to place the video out on the legacy video lead. However, a HDTV set must convert the analogue video signal back to digital in order to digitally resample (up-convert) the picture, especially when it comes to pure digital sets such as a plasma or LCD display that have a fixed native resolution. This digital to analogue and analogue to digital process both causes the picture to degrade a little. The same can be said for audio, for example an audiophile would not go about ripping a CD by playing a CD in a standalone CD player and recording it on their PC through their soundcardâ€™s analogue line-in jack.
A DVD player with a built in HD up-converter overcomes this issue by resampling the image to a HDTV resolution such as 720p, which can be sent to the digital HDTV display using a DVI or HDMI link. This eliminates the quality loss caused by converting the picture to analogue using analogue video connections.
Note that even if your HDTV is a CRT set and you use analogue video leads, most HDTV sets will still convert a standard definition analogue picture to digital in order to perform the HD up-conversion process to display the image.
On the other hand, if your DVD player has a DVI or HDMI output connection and relies on the HDTV set to do the up-conversion, then whether the HDTV set or the DVD player does the resampling, there will be little benefit in the picture quality since the video will remain in digital from the DVD player to the TV in either case.
I came across an article on Howstuffworks.com that goes more in detail.