The Sony PS3 supports 1080p and for a while claimed to be better than the XBox 360 for this reason. The XBox 360 now has an update so it also supports 1080p high definition resolution.
To understand what this means, let's do a rundown of some TV resolution terms. First, the P vs I. P means "progressive" and in essence it means that the entire screen paints at once. I means "interlaced" and it means that half of the screen paints (say rows 1, 3, 5) and then the other half of the screen paints (say rows 2, 4, 6). P is generally preferred over I for this reason, and generally costs more too :)
Now, the number part. Traditional TVs were 480 - i.e. 480 rows of "dots" that made up the image. If you look really closely at a traditional TV, you can see those dots, and of course if you had a lot of time on your hand, you could sit there and count the rows :) There being only 480 of them, that made the image rather grainy.
When you step up to 720, you have almost double the resolution. Double the number of rows. This gives you a much higher quality image to view. Many broadcasts are done in 720p rather than 1080i for high definition, because the progressive gives a better quality image when the item being shown is moving, so sports shows do better in 720p.
Currently (as of November 2006), no TV broadcast is being done in 1080p, and only a few TVs support 1080p. 1080p is more the "high end movie production", and is what movie producers use to shoot their digital scenes. Still, there are of course a few people who do have those high end TVs, and now the XBox 360 supports their systems.
Both HD DVD and Blu-ray DVDs support 1080p high end movies. Note that if you buy a player, you need to check its output options. Some HD DVD players will not output in 1080p - they will only output in 720p or 1080i. You want to make sure your player supports the TV set you are using.
So if you're lucky enough to have a 1080p TV, make sure you go online with your XBox 360 so you can get the update to support that!