Just to show my level of geekness...
HDTV is more than just the "TV set". HDTV refers to a set of broadcast standard resolutions that exceed the 480 scan lines that defined NTSC's (analog) signal maximum. In general, this refers to "720p" (720 scan lines, done progressively - i.e. line 1, then line 2, etc.), "1080i" (1080 lines, but the lines are interlaced - lines 1,3,5,... are drawn first, then lines 2,4,6,8,... are drawn, usually with each half drawn in 1/60th of a second - so a whole frame takes 1/30 of a second, and its up to our eyes to "meld" them together - NTSC signals work the same way), and 1080p (1080 lines, progressive). And don't even get into different frame rates - heads will explode.
There is also a 480p resolution, which means the 480 NTSC standard lines are drawn progressively, as opposed to 480i (which is sometimes how NTSC is referred, albeit incorrectly since it more properly refers to a digital signal). This is considered "enhanced definition" or EDTV. DVDs with progressive scan output can do this.
All of these are referred to "Digital TV".
ATSC does not generally support 1080p - that is left to other media like Blu-Ray discs.
Any device with an ATSC tuner is capable of "downscaling" an HDTV signal to 480i or 480p depending on the TV/monitor being used to view it.
The whole "Digital TV" conversion is for local broadcasters to stop their old NTSC transmissions and only use ATSC. Anyone who relies on a TV with only an NTSC tuner and receives their signals over the air with an antenna need to either upgrade their equipment, or at least get an external ATSC tuner - which is kind of a like a cable box, but you hook your antenna up to it.
People who get their signals via cable or satellite are all set - their converter boxes are doing all the work for them already.
Edit: a bit more on HDTVs - some TVs are rated for 720p, others 1080i (or more commonly now 1080p). Both are capable of displaying the other - they just convert it to whatever the TV needs. Its a matter of preference as to whether you think the advantages/disadvantages of one over the other are important to you...but that's a whole 'nother discussion, and my DD is waiting for me to play Rock Band with her.
