HD = high definition = high resolution = high definition.
Because the iPhone 4 didn't come out when the first generation iPad came out, the latest one is the iPhone 3GS, and the game resolution on the 3GS is very low (compared with the iPad), so many games need to be re-made in the iPad version (in fact, the screen resolution is only improved). In order to distinguish it from the iPhone version, marking a high-definition logo can simply mean "iPad only" (if it is forcibly installed on the iPhone, the screen will be biased and it will not operate normally)
However, due to the improved screen definition of iPhone4, many softwares already support both iPhone and iPad, so many iPad softwares are not standard HD.