Most importantly some games will simply not work on newer hardware, a few may even straight up crash the system entirely. Keep in mind that some games that the site tells you you can run, may not run, and vice versa. The result should tell you what specs you have. To find out what kind of card you have, pixel shader ver, vertex shader ver, etc, you can go to System Requirements Lab and check any game.
A higher pixel shader can be used but the frame rate may drop to like 10FPS. Vertex shader (version required by game or higher) is required or the game won't run at all. Hardware T&L is not actually necessary, but your game might look crappy. Your PC (with the exact specs) might not run the games or might run them crappily (minimum req usually mean with choppy framerate). The system requirements here are taken from the developers, game sites, and other sources. Just remember that some pc's with integrated graphics may well reach the requirements but still have issues running games (portal, looking at you.etc) Odds are, people looking in this list for games are on laptops with integrated graphics and outdated desktop computers.
This list is basically for people who think they have crappy and a slow computer that can't play recent games.
