BluRay allows significant more space usage on a single disc. You can basically store 6 times as much an a BluRay disc than on a DVD. This allows the BluRay disc to not only store all of the information for high resolutions of films, but it allows them to store extra features like behind the scenes stuff, and outtakes and the like. DVDs could generally get high enough resolutions that normal TVs you can't tell the difference. However, on HDTVs, the higher resolutions make a significant difference.
Before I got a BluRay Player, the only HD that made much difference to me was sporting events, because most television isn't filmed in HD (although that is changing). Now, any film that was filmed at higher resolutions, looks better on my TV.
Here's an example. I got the BluRay release of Band of Brothers last week. The original 6 disc set, looked great, but had very little in the way of extra features, and they all went on a separate disc. In the BluRay set, they still have six discs (which surprised me), but the picture quality is remarkably better, and for each episode, they have an entirely new track of Picture-in-Picture video, where you get interviews with the original soldiers as the episode goes along. It's amazingly interesting, and basically shows how there's more than twice as much as there was before on each disc.
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I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.