ecoustics has posted a brief but very useful article on how TV and HDTV work, including a simple explanation of the different digital formats:
480i: Picture transmits at 60 interlaced fields per second (30 frames per second). Same number of scan lines and frames per second (fps) as analog, but provides a slightly improved image merely because of digital transmission method. Provides surround sound-capable digital audio that matches CD-quality Known as Standard Definition Television (SDTV)
480p: Same number of scan lines as analog, but sent progressive-style (60 complete fps) resulting in an even more improved picture. Capable of Dolby Digital Audio. Known as Enhanced Definition Television (EDTV)
720p: Higher resolution picture with 720 scan lines, sent at 60 complete fps. Provides Dolby Digital 5.1 Surround This is HDTV
1080i: Even higher resolution (1080 scan lines), but fewer frames per second. (60 fields per second, equal to only 30 complete fps). Provides Dolby Digital 5.1 Surround This is HDTV
1080p: This is the ultimate format goal for the future: the best of both worlds with maximum scan lines and maximum fps. No broadcasters have adopted this format, and not many TVs can display it properly.