DVI stands for "D"igital "V"ideo "I"nterface and provides a digital link between your digital, hi-def cable signal and your digital TV. In other words, from what I understand, you lose a Digital-to-Analog conversion step using this connection, thus giving you a better picture.

The "H"igh "D"efinition "C"opy "P"rotection allows you to receive encrypted broadcasts from providers who believe you're going to copy their hi-def signal otherwise. The thinking is that if you're watching a hi-def transmission of a movie, you won't be able to copy that to a disc and produce a DVD that's higher quality than the regular release. It's sort of related to why there isn't a standard digital connection for DVD-A and SACD.

The second Q&A on this page from the Secrets website answers a very similiar question much better than I can:

http://128.121.62.219/qa/qa2003/qa375.html