From Microsoft:
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DirectX® is the multimedia system foundation for the Windows operating system. Using DirectX, programs can take full advantage of your computer to give you the best possible multimedia experience. >>
DirectX is a series of Windows APIs that accelerates multimedia functionality that comprises of DirectDraw, Direct3D, DirectPlay, DirectMusic, DirectSound and DirectInput.
Probably the most important are DirectDraw (for 2D graphics), and Direct3D.
One of the main advantages in the early days of DirectX was that it provided a standard baseline for multimedia functionality in things like video card drivers.
DirectX is especially important under Win2K and WinXP as drivers do not have direct access to the hardware (as was possible under DOS, Win3.x and Win9x). Drivers used to be able to get the best performance by having direct access to the hardware.
More from the Microsoft DirectX Overview:
Microsoft DirectX® is an advanced suite of multimedia application programming interfaces (APIs) built into Microsoft Windows® operating systems. DirectX provides a standard development platform for Windows-based PCs by enabling software developers to access specialized hardware features without having to write hardware-specific code. This technology was first introduced in 1995 and is a recognized standard for multimedia application development on the Windows platform.
What DirectX Does and How
Simply put, DirectX is a Windows technology that enables higher performance in graphics and sound when you?re playing games or watching video on your PC.
At the core of DirectX are its application programming interfaces, or APIs. The APIs act as a kind of bridge for the hardware and the software to "talk" to each other. The DirectX APIs give multimedia applications access to the advanced features of high-performance hardware such as three-dimensional (3-D) graphics acceleration chips and sound cards. They control low-level functions, including two-dimensional (2-D) graphics acceleration; support for input devices such as joysticks, keyboards, and mice; and control of sound mixing and sound output. Because of DirectX, what you experience with your computer is better 3-D graphics and immersive music and audio effects.