The "i" in 1080i means "interlaced. This means that every 60th of a second, the image has 1,920 pixels of width, and 540 pixels in height (a 16x9 aspect ratio). The next 60th of a second, a slightly different 1,920x540 image is shown. Because all current HDTVs are progressive, these interlaced images are weaved together by the television to create a full 1,920x1,080 image (or whatever the native resolution of the display).
Blu-ray discs are usually 1080p. This means that ever 60th of a second the image is a full 1,920x1,080 pixels. With film-based content there is no resolution difference between 1080i and 1080p, as long as the display de-interlaces the 1080i correctly. Native progressive images (1080p/720p) can look better with fast motion due to their higher framerate.