HDTV comes in two distinct flavors, 720p and 1080i, and, in the case of HD-DVD and Blu-Ray, 1080p. The 720p and 1080i formats are used by the various networks, though none broadcast more than one.
The numbers in each format refer to how many vertical lines of resolution a screen can display. In addition, video with the larger vertical resolution also contains more horizontal resolution, as well. For example, video with a vertical resolution of 1080 lines has a horizontal resolution of 1920 while a vertical resolution of 720 offers a horizontal resolution of only 1280. Of course, lines and pixels aren't the only factors in play here.
The letter "P" indicates progressive scanning (rendering all lines in an image in one scan) while the letter "I" indicates interlaced scanning (scanning the odd and even lines in separate passes). 720p has fewer lines of resolution, but smoother moving video. 1080i offers greater resolution, but less clarity with faster movement. In these two cases, their strong and weak points mostly cancel each other out. However, that will eventually change.
1080p combines the best of both worlds: smooth motion and excellent vertical resolution, though no TV stations currently use the standard. This will eventually change, so buying a TV that supports this standard will prepare you for the future. In additon, you'll be ready for the newer HD disc formats.