My high-definition television runs at 1080 lines interlaced, with a 16:9 aspect ratio.

There is a competing standard of 720 lines progressive-scan, with a 16:9 aspect ratio. My TV doesn't display this rez, but my high-def-decoder box will automatically convert a 720p image to 1080i on-the-fly so that my TV can display it (with slight loss of quality in the process).

There are also variations on these standards such as 540 lines progressive (same scanrate for the CRTs as 1080i).

When receiving high-def signals (both from satellite and from over-the-air highdef broadcasts), you will often get a "mix" of these formats. Either your TV will display all of the possible resolutions, or your high-def decoder box will allow you to set a switch which forces it to convert all of the content to 1080i.