What is 1080p on a TV?

the 1080 number refers to the number of lines of video vertically (top to bottom) on your TV. The "P" refers to progressive scan.
You have 2 types of scanning:
Interlace: Which is where your lines scan the even lines first (540 lines) then the odd lines next (540 lines), then the even line, etc. This happens 60 times per second which means your complete picture is refreshed 30X per second.
Progressive: With progressive scan all 1080 lines are scanned 60X per second which means your picture is refreshed twice as often per second.
This results in more smooth motion and greatly enhances your viewing experience. The 1080p is the best HDTV.