Umm... isn't 720p normal? 1080i and 1080p is HD.
HD can mean all of those: 720p, 1080i, and 1080p
The number is the vertical resolution (the number of pixels high).
720 means 1280x720 | 1080 means 1920x1080
The letter indicates if it's progressive or interlaced. Progressive (p) means all the pixels change every time the screen is updated. Interlaced (i) means that every other row changes with every screen update. (Progressive is better).
a better description:
"The lower-case "i" appended to the numbers denotes interlaced; the lower-case "p" denotes progressive. With the interlaced scanning method, the 1,080 lines of resolution are divided into pairs. The first 540 alternate lines are painted on a frame and then the second 540 lines are painted on a second frame. The progressive scanning method simultaneously displays all 1,080 lines on every frame, requiring a greater bandwidth."
http://en.wikipedia.org/wiki/High-definition_television#Advantages_of_HDTV_expressed_in_non-technical_terms