What is the difference between normal graphic card and HD graphics card

A HD graphics card will usually have higher Memory and Faster Chips to allow Gaming at 720 or 1080 resolution and higher.
It's also have added processing power for High Definition Videos, meaning the playback support for 720 or 1080 encoded videos.
Which is not usually there in standard non HD GPUs.
 
HD is just a fun add on bit for the name to make it seem faster, nVidia uses GT, GTS, and GTX, AMD has HD before all of their current model numbers, and the intel IGPs in the core i series processors are their first ones that dont suck horribly, those are referred to as HD GMA by them.