Remastered DVD in HD


I have noticed Re-releases of older DVD movies stating in the backcover of the DVD that this Movies is Remastered in HD. What does this mean? Can anyone shed some light about this DVD. Are these DVD's True HD DVD quality or will they look better than the original release? Thanks.
avraj
Excellent posts Elizabeth and John z.On my new Marantz 1900, I actually prefer many movies on it rather than on HD cable.I just finished watching King Kong and also The Mexican and all I can say is,"WOW!".When the original program is recored in HD,then it does look much better.And this on my Fujitsu 50".
Thanks for the explanation Elizaberth and John. I have another question. Is it better to buy the remastered DVDs, for example, the Patriot. Will studios re-release such title in the newer format? Once again thanks for the response.