To see the benefits of HD you need to watch something that’s been shot on an Digital HD camera, or film that’s been digitised or CGI rendered at HD resolution, the best is 1280 and then 720, SD is 576. The numbers refer to the amount of pixels vertically, the more pixels the more information in the picture, just like a digital image on your camera or computer screen. You also need a HD playout device eg: set top box, ps3, blu ray player etc connected to the HD TV via HDMI, scart will never display HD. HD normally has less compression, Blu ray has virtually no compression. HD also refers to the audio which is mostly Dolby 5.1, again to hear the benefits you need the correct kit and speaker set up.
Most Sky HD ads are shot in slowmo, this is a clever way to help with image compression, digital encoders hate lots of colours with fast movement. Grass and Football has always been challenging for digital TV, hence why Sky Sports pushed HD so heavily.