HDTV is High Definition Television. HDTV refers to any TV set capable of enhanced resolutions.
Despite the myriad of display technologies that encompass HDTV, there are really two basic types of display - those that present direct pixels and those that present scan lines.
CRT technology that presents the picture as a series of lines. Regular NTSC has 480 active scan lines displayed in an interlaced fashion, 480i. HDTV can enhance 480i by making it 480P (progressive scan). HDTV goes up to 720P and then 1080i.
Fixed pixel is a display type with resolutions measured like a computer monitor. A high-resolution TV with fixed pixel display might be 1024x768. The fixed pixel display doesn't have lines scanned by an electron beam, but rather a grid of separate dots that can be colored according to the source video signal. It's a different method of displaying video but isn't necessarily superior to scan lines.
If you're looking for a new TV with a picture larger than 32", you should be looking into your widescreen HDTV options.