p- progressive scan
i- interlaced
HD content is always broadcast at 30 frames per second.

1080p content is played back at native frame rate, while 1080i is played back at 60 fields per second (a field is the technical term for an interlaced frame).

The duplicated frames are displayed separately, faster than the human eye can detect them.

The key differences are:

1080p (progressive scan) mode may appear to be sharper, and fast-moving action can be easier to watch. This mode is used for Blu-ray discs and some games consoles, and is known as Full HD.
1080i (interlaced) mode may appear to flicker or blur more during action scenes or sports. Some terrestrial TV in the UK and USA is broadcast in 1080i; the rest is broadcast in 720p.
In practice, many people do not notice the difference between 1080p and 1080i. If you have a large HD TV, you may prefer 1080p, but the difference is often negligible.

Glad I didn't have to type that^