It is a new standard of television that not only inclused better resolution but native 5.1 surround sound in the feed. A tv must say HDTV ready/compatible not EDTV or progressive scan capable (because there is a standard definition progressive scan at around 480P. 480 lines of progressive video (480 lines per frame). 480p60 refers to 60 frames per second; 480p30 refers to 30 frames per second; and 480p24 refers to 24 frames per second (film source). Usually refers to 720 x 480 (or 704 x 480) resolution. A standard digital television is capable of this.
720p means that the resolution of the picture is 1,280 vertical pixels by 720 horizontal pixels and p stands for progressive scanning. Progressive scanning offers a smoother picture as 720 horizontal lines are scanned progressively or in succession in a vertical frame that is repeated 30 times a second (Google) Only HDTV
1080i means that the resolution of the picture is 1920 vertical pixels by 1080 horizontal pixels and i stands for interlaced scanning. Interlaced scanning is based on the principle that the screen shows every odd line at one scan of the screen and then all the even lines in a second scan (Google) Only HDTV
Both are possible depending on your monitor.
Most new HDTV's come with either 720P or 1080i capability (usually a separate tuner is necessary). Some very high end tv's (have 1080P capability but very expensive)
1080p means that the resolution of the picture is 1,920 vertical pixels by 1,080 horizontal pixels and p stands again for progressive scanning. This format works on the same principle as 720p; the only difference is that in this type there are more pixels and the resolution is better. (Google) Very rare indeed.
Good overview
If you have a fairly modern PC you should have no problem playing 720P (Anything over about 2000mghrtz (Intel or AMD equiv) with a decent video card (I am talking less than 9600 pro) but 1080i requires a little more horsepower (Anything over 3ghrtz (Intel and AMD equiv) with 32meg graphics card (9600pro and up)
Some download samples of 720P and 1080i