This should answer all your questions DVI/HDMI primer Very easy reading
They're both digital connections and can be used with upsampling DVD players to avoid extra D-A and A-D conversions, especially useful with digital projectors.
HDMI also carries audio signals (main difference). It is becoming more popular and probably will replace DVI in the future.
If you have a DVI projector and a HDMI DVD player (as I do) a HDMI-DVI adapter can be used for the video.