There are plenty of displays with 1080 horizontal lines of resolution, and they display 1080i just fine.
1080i only shows 1/2 of the picture every 1/60th of a second. 1080p shows a full picture every 1/60th of a second, so you get twice as many actual pixels per second compared to 1080i.
720p and 1080p are ideally suited to fast motion, as in sports, because you get a more frames per second. 1080i has more detail than 720p but there may be blurring during fast action.
Anyway, as I understand it, there are no actual 1080p sources in existence at the moment, and I'm not really sure if there will be. I also think that no current sets can actually display 1080p programming, despite what the manufacturer claims.