i = interlaces. That means you get half of the picture lines in one frame, and the other half the next.
p = progressive. That means you get all lines of the picture in every frame. As such, twice the data is being 'pushed' through the 'pipes'.
1080p = blu-ray = technically the best HDTV picture one can have.
BUT...there's many other variables:
- size of your TV
- quality of your TV
- quality of signal (cable and satellite is highly compressed, for instance)
- frame rate of the signal
There are many technical arguments to be had, but for most average TV watchers, they won't usually be able to tell the difference between 720p and 1080p from their couch 12' away from their 40" TV.
I was all gung-ho with getting Blu-Ray set up with the new TV but then I connected my old DVD player via HDMI to take advantage of the up-converting. If I sit 2' in front of my TV, I can tell, but I never do and found, at least from the couch, I'm not sure I'd fully appreciate 1080p even if I had it.