From LQWiki

3D graphics acceleration (sometimes 3D acceleration or Hardware 3d acceleration) refers to software which does 3D rendering using special functions of a video card to accelerate the rendering. Most recent video cards support some form of this acceleration.

3D Graphics Acceleration on linux has been an exciting field in the last few years. For Linux the most 3D Graphics activity has been and is currently centered around NVidia 3D video cards and their corresponding linux drivers. NVidia has released a set of mature linux drivers which are compatible with virtually all NVidia video cards. Previous to the release of the NVidia drivers, linux was sorely lacking in 3D graphics performance. The linux drivers are very mature although they are not open-source. Ati has a similar set of drivers whose maturity lags behind NVidia but the gap is closing.

Normally applications don't directly use these features of the video card. Instead, they use a 3D graphical language API, such as OpenGL, Glide or DirectX. The libraries that implement this then deal with hardware acceleration transparently to the applications, meaning they fallback on a software method if the driver of the video card doesn't support some feature.

In Linux this can be done by the Direct Rendering Infrastructure. DRI was originally created as an extension to X, but can also be used without it (see fbdev/DRI drivers from the Mesa3d project as an example of this). The most used 3D API in linux that supports hardware acceleration is OpenGL, see that page for more info on enabling it.