DirectX's true intent is to make game programming as simple as possible by providing a hardware-independent abstraction layer above the myraid of blazingly fast (and immensely different) graphics cards. Another advantage is that DirectX drawing and screen display routines are a lot more minimalized and boiled down than GDI calls. Mind you, DirectX games are not portable across platforms (Wine does have some DirectX support, but no one seriously considers that when making a game to bring to market). With some abstracted functions, you can work around that. DirectX is also an underlying technology of the upcoming Xbox game console.
The first flagship game to use the Direct X technology was actually Doom, a non-DOS version of the famous first person shooter. It required DirectX 1.0, which was just a fledgling product that you could download from the Microsoft website. I inadvertently got it the day it came out. DirectX really didn't mature until release 3 (for NT 4, and most DirectDraw items, which came late), or release 5 (the first excellent, very clean and widespread release). A lot of hardware vendors today provide DirectX aware drivers for the hardware, making the game developer's life just a bit easier.