Blu-ray and HD-DVD plays High Definition Video, that is, either 720p(1280x720 resolution) or mostly 1080p (1920x1080). Currently each of these formats has about 130 titles in their basket.
The workings are totally different from a DVD, that is, you need a HDCP graphics card along with a HDCP monitor (so you cannot make rips off it). You would also require a high end machine to decode the video, without which it would start dropping frames (stuttering video). They however work well on standalone Blu-ray/HD-DVD players.
I have not experienced blu-ray per se, but I have got some high definition movies on my HDD. Amazing clarity, much much much better than DVD. I've got like 5 movies in High Definition...