NVIDIA

NVIDIA is the world leader in visual computing technologies and the inventor of the GPU, which generates interactive graphics on workstations.

VDPAU
VDPAU (Video Decode and Presentation API for Unix) is an open source library (libvdpau) and API originally designed by NVIDIA for its GeForce 8 series and later GPU hardware, targeted at the X Window System on Unix-based operating systems (including Linux, FreeBSD, and Solaris). This VDPAU API allows video programs to offload portions of the video decoding process and video post-processing to the GPU video-hardware.

See - http://en.wikipedia.org/wiki/VDPAU

PureVideo
Nvidia PureVideo is a hardware feature designed to offload video decoding processes and video post-processing from a computer's CPU hardware to NVIDIA's GPU hardware series GeForce 6, GeForce 7, GeForce 8, GeForce 9, GeForce 200, GeForce 400, GeForce 500 ; GeForce M series (formerly known as GeForce Go); and Nvidia Quadro series. PureVideo is designed to work with media playback software. NVIDIA's device drivers for Windows XP, Windows Vista and Windows 7 are PureVideo-enabled; with the appropriate (PureVideo-enabled) application software, the NVIDIA driver will automatically use whatever hardware-acceleration is available on the NVIDIA display-adapter.

All software HD DVD/Blu-ray players, as well as most software DVD players, are PureVideo-enabled. Microsoft's Windows Media Player and Windows Media Center also supports NVIDIA's PureVideo technology. NVIDIA also sells its own PureVideo decoder software (which is a source of confusion, as NVIDIA's decoder is not required and not used by third-party players), which serves as a DVD player with advanced post-processing capabilities. The degree of PureVideo's capabilities varies by generation.

On 2008-11-14 NVIDIA released a beta version of a closed-source device driver and open-source API called VDPAU (Video Decode and Presentation API for Unix) with PureVideo support for Linux, FreeBSD and Solaris.

http://en.wikipedia.org/wiki/Nvidia_PureVideo

Examples
Here are examples of software using VDPAU.

Mplayer

The error when you NOT have one of these new video cards...

[vdpau] Error when calling vdp_device_create_x11: 1