HD is simply refering to the resolution. i'm pretty sure all computer monitors, CRT or LCD are high def because they typically exceed the High Def resolutions of XXXX x 768 and XXXX x 1080 (the horizontal resolution varies by product). the 1080 is known as true HD.
i would recomend using the DVI-D cable (it is typically white on both ends) if your GPU/TV supports it.
i was wondering this too, my pc always asks me if my monitor is hd, i always say no. I have a dell 17 inch ultrasharp, im thinking it is, highest res is 1280xxxxx, i forgot