The difference lies in how the display lines are scanned. While both resolution standards display 1080 vertical lines, with 1080i the lines are "interlaced" - meaning the odd-numbered lines are painted on the screen first followed by the even-numbered lines.
While 1080p video is definitely preferable to 1080i, it’s also worth noting that unless you’ve got above-average eyesight, you probably won’t be able to notice a difference between the two on smaller screens.