DirectX is a collection of Application Programming Interfaces (APIs) that grew from a host of other APIs that had titles starting with the world Direct, such as Direct3D, DirectSound, DirectDraw etc. It is used on Microsoft systems such as the Windows operating system, and the Xbox 360 console. DirectX is used by developers for multimedia tasks which include game programming, video processing and computer aided design. Direct3D is part of the DirectX package and is widely used for game development to create 3D graphics environments for titles used with Microsoft windows and both the Xbox consoles.
Other DirectX related glossary:
DirectX Media Objects