DVI stands for Digital Visual Interface. It is an all digital link between a video/audio source such as an HDTV Set-Top Box and a display device such as an HDTV. The DVI link provides an uncompressed digital stream at rates up to 5 Gbps between the two devices. The DVI link does not contain audio, so audio is still needed to be connected from the Set-Top Box to the HDTV or home theatre system. One advantage of DVI is that the link allows graphics to be sent along the link as well. This allows the user interface from the Set-Top Box to be displayed on the HDTV.
HDCP stands for High-Bandwidth Digital Content Protection. HDCP is the copy protection standard that is tied to DVI.
HDMI stands for High-Definition Multimedia Interface. HDMI is the next generation of DVI. The main difference between HDMI and DVI 1.0 is that HDMI adds audio to the DVI link and is a smaller connector. The HDMI interface will be backwards compatible to the DVI 1.0 interface, meaning that you can connect up a Set-Top Box to an HDTV, where one has DVI 1.0 and the other has HDMI. Most new HDTVs have HDMI. Those that don't most likely are equipped with DVI, which is backwards compatible.
For more information visit: http://www.hdmi.org/learningcenter/