A DVI cable only supports digital video, not audio. Whereas, an HDMI® cable supports both digital video and audio. Because a DVI cable is capable of supporting video only, it also is necessary to connect an audio cable to your equipment to get any of the accompanied sound. With an HDMI cable, both the audio and video are transmitted using a single cable.
Another difference is that HDMI incorporates High Definition Content Protection (HDCP), a security measure to prevent the copying of copyright-protected material.