It means that the games are already taking advantage of higher resolutions (sharper objects, more detailed appearence)
P means progressive, as in the game is showing 1 frame at a time only, instead of I (interlaced) where each frame is actually a split of 2 frames.
480P would be comparable with a 640x480 computer resolution, 525P is a tad less than 800x600, 720P is about 1028x768 and 1080P will be around 1280x1024.