P stands for Progressive. I stands for Interlaced.
1080p is 29.97 frames every second. 1080i is 59.94 fields every second. There are two fields, an upper and a lower. Each field is half of a frame, containing every other line of the frame.
The problem with recording interlaced is that when something is moving, two fields that are supposed to line up will be offset. The camera will read the first field, then something moves, and the next field will be different:
So 1080i is basically 1080p, but with motion issues. I never shoot interlaced, progressive is the way to go. Interlacing was needed years ago when they didn't have enough power to get enough progressive frames per second, but it's pretty much useless now. I don't know why it's still used. So when you have a choice, choose 1080p. You can read more into it but that's it in a nutshell.