I've had a PS3 since 2008, before that I had a similar "What's the big deal with BluRay" attitude, only the deal wasn't as big then as it is now that we're getting more and more releases on BluRay.
Long story short when it comes to movies and a 1080p TV you really see the difference like Sigz said, in my case to the point of getting too spoiled and being unable to enjoy my old normal DVDs anymore. Even on new DVDs quality now looks similar to quality of cable TV broadcast of widescreen "HD" shows and movies. BluRay quality is something you can only get from Blu Ray disc.
But what really sweetens the deal -especially for a music fan- are concert BluRays, so far I only have one cause only one of the bands I like has released a concert BluRay but luckily the perfect one to do so. Porcupine Tree Anesthetize Blu Ray. If you're interested in PT and wanna know what's the big deal with BluRay then get this release, it blows me away every time, Wilson being an established master of audio mixing and sound production is a strong enough aspect to experience in such clarity and quality, let alone the visuals and the lighting on the stage itself.
I was most excited when DT's Live at Budokhan was announced for release on BluRay but surprisingly I haven't had the chance to buy it yet. Hopefully very soon. I heard people praising it and it wasn't even shot in HD, imagine how amazing the new BluRay is going to be, especially with how awesome the music and the visuals have been on this tour, mouthwatering goodness.