720p is what most real "HD" broadcast are in (native format) like the HD channels for cable, fios, turbohd. 720p is 1280x720 resoltuion (as an average, can sometimes be more)and 1080p is 1280x1080 (as an average, nowadays its a higher resolution) resolution, both are in progressive format which "paints" the image sequentially on the screen instead of every other line and then goes back like interlaced does. progress has less "flicker" and is typically referred to as a "smoother" picture. if you buy a 1080p tv , its native is 1080i and 1080 not 720p. i used to be that this caused an issue with 720p medium, because the 1080p tv would have to downgrade to 720p and would actually produce a sub par 720p picture. but with newer tv's they have more robust video software and hardware, that solve these issues.
also 1080p tv's will accept the 24fps(most do, not all) , that bluray offers instead of playing the normal 60fps or 30fps, you get from normal digital tv or dvd's. another feature to remember is that (i believe) the only tv''s that operate at 120hz instead of the old 70hz are 1080p tv's so if you want that INSANE 3-D hd experience from blu-ray and super duper HD channels you need ( I believe) a 1080p tv. (720p tv's may have the hardware by now, not sure)
also the bigger the tv, logically the more resolution you will need.
remember, not all 1080p OR 720p tv's are the same. YOU GET WHAT YOU PAY FOR!
hope i helped.