720p = resolution of 1280 pixels x 720 pixels, drawn progressively. What all that mumbo-jumbo means is that the system can draw 1280 dots per line, 720 times, in one frame. The letter "i" is used when the system does not draw the screen all at once, but rather it draws every other line in 1 frame, and then the remaining lines in the next frame.
1080p = resolution of 1920x1080, same as above just change the numbers.
Personally, 720p is more than fine. I have played PC games in both resolutions and only a trained eye can really spot the difference.