It's basically the name of a certification programme for digital equipment. There's four logos "HD ready", "HD TV", "HD ready 1080p", "HD TV 1080p" - assuming the manufacturer assigns them properly.
Anything at 720p or above means it's HD - but there are different types - If it's just "HD ready" that means it can support 720p and 1080i. Essentially those numbers are the measurements of the screen, same idea as a computer resoluton (1280×720 and 1920×1080). P means progressive and I means interlaced, that's an entirely different topic but it's really just different ways of displaying the picture.
Anything that plugs into a HDMI cable will be HD or upscaled to that, it can be pretty intricate though and would depend on the source material though as far as your concerned everything Blueray is HD and a fair chunk of DVDs can be upscaled to that.
Finally for TV channels there are three ways to go: Sky box, BT Vision/Internet TV box or Freeview and even then only certain channels will broadcast in HD and you may need to pay an additional subscription for some of them. Apparently Freeview HD isn't in the are yet but will be round about he 16th of June. That link also has a list of TVs with builtin in Freeview that are HD compatible.
EDIT: One small note a like-for-like (you get different specs but they don't really affect price much) £5-£15 HDMI/audio cable is just as good as a £50-£75 cable, better is some tests actually. The higher pricing is designed to appeal to those people who think more expensive is automatically better.
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