I currently have an SDTV and am thinking about getting an HDTV. I find the subject of HDTV confusing though. Whenever I see a HDTV in the store it says HD-Ready. I see HD-Tuners and HD-Boxes but don't understand what they are used for. I want to be able to use the HD capability of my Xbox 360. What exactly should I be looking for when I purchase a HDTV?

HD ready means it can accept an HD signal and display it, like from the 360 or a HD cable reciever. It just means that the tv can not tune hd over the air tv channels, like you local tv stations with just an antenna, the is what the hd "tuner boxes" are for.

I saw an HD-DVD player. Any chance the Xbox 360 is capable of playing HD DVD's the same way a HD-DVD player can?

yep, there is a hd-dvd add on drive for 199$

the xbox 360 is capable of delivering high definition up too 1080p. but it cannot play hd dvd movies because th discs are different.
you have to purchase the xbox 360 hd dvd add on for around $200.
I have it and its awesome though.

if you connect it by an svga lead the 360 will play normal dvds in hidef (upscaled) it will not work with the component leads due to a law stopping it

If you buy a HDTV then you can then select your xbox to output for example 720p signal and you will actually notice a big image difference, compared to a standard non hdtv compliant tv.

But this doesnt work for movies that easily and then you can buy the addon HD-drive from MS.