What is the difference between 480p 720p and 1080p?

The numbers refer to the number of lines that form a television picture. The "p" stands for "progressive scan". They refer to the signal format and all HD televisions should be able to handle any of the formats.
Standard definition television in North America uses 480 lines but the "p" indicates that the source is likely to be a computer or other non-broadcast source. Broadcast standard definition television uses 480i which is a lower data rate and requires two fields to generate a single frame of the picture. 480 line images are also normally in a 4 : 3 aspect ratio.

High definition broadcasts use either 720p or 1080i. Both are considered to be full HD and both use the same data rate to deliver a signal. In these cases, the image is made of 720 or 1080 lines. The aspect ration is always 16 : 9.

1080p is the same resolution as 1080i but uses progressive scanning to build a complete frame on every pass. This requires twice the data rate of 1080i (for the same field rate) and is not currently available as a broadcast format. It is seen on local sources such as Bluray or games consoles.