DVI stands for Digital Visual Interface. This is a high-bandwidth connector for digital video connections capable of exceeding the bandwidth required for 720p and 1080i video signals. It's compliant with HDCP so the format should offer a certain amount of future proofing.
It is important when you look for a new HDTV or DVD player to look for a DVI (or HDMI) interface. There aren't very many DVD players with DVI yet and the ones that exist are expensive. Look for DVD players featuring this technology to decline in price in the near future.
component outputs and switch to DVI you'll see a difference in resolution by about 15% improvement. Fewer artifacts from the decompression of the video source will result in a cleaner picture with less wiggly lines around high-contrast images.
It is already rumored that in the future non-HDCP video signal delivery methods (including analogue cabling like component) might be penalized by the entertainment industry. They are rumored to be in favor of adding downscaling resolution from these video sources, hence giving only HDCP video methods a monopoly on the best possible image quality. As unlikely as it is that they'll add downscale information to sabotage video quality for non-HDCP, you shouldn't spend the money on today's HDTVs without DVI or HDMI video connectors.
DVI connectors come in two flavors - DVI-D and DVI-I. DVDI-D is digital only and DVI-I also supports analogue connections.