1080i is the most common HD resolution, and is the default setting for most cable and satellite boxes. CBS, NBC, and most HD cable channels are natively 1080i. ABC, Fox, and ESPN, are 720p.
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.