1080i and 1080p?

The i stands for interlaced, and the p stands for progressive. In a tube-based television, 1080i sources get "painted" on the screen sequentially: the odd-numbered lines of resolution appear on your screen first, followed by the even-numbered lines--so quickly your eyes see them as one picture.

Progressive-scan formats such as 480p, 720p, and 1080p show all of the lines of in one pass, which gives a smoother image. Fixed-pixel TVs, including plasma and LCD flat-panel, convert interlaced signals to progressive scan for display.

If you are buying a small TV (say, under 40 inches) you probably won't notice a difference between 1080i/p, or indeed 720p.

There is very little 1080p stuff to watch, except Blu-Ray. HDTV is still mostly 1080i.