Communication between Wi-Fi devices isn't specifically new. The Nintendo DS, for instance, has had device-to-device Wi-Fi interaction for some time, but the technology is proprietary.
The Wi-Fi Alliance differentiates Wi-Fi Direct by certifying the standard, ensuring interoperability. Devices stamped with the Wi-Fi Direct certification don't need wireless networks, as they essentially become micro-hotspots.
This technology will conceivably allow devices like an Eye-Fi memory card to directly beam an image to a wireless printer. Since Wi-Fi Direct is largely software based, many recent devices should be upgradeable.
Speeds for Wi-Fi Direct are based on 802.11b/g/n channels, so we're looking at intra-device throughput at rates upward of 300Mbps. Range will also be a major selling point, and it's reasonable to expect that future Wi-Fi Direct devices will eventually achieve distances similar to our home wireless networks.
Bluetooth will undoubtedly be the first technology to suffer as a result of Wi-Fi Direct. Although Bluetooth is aimed, almost universally, at close connections like headsets, it will be hard to trump the speed of Wi-Fi direct. Additionally, Wi-Fi Direct would use the same transponders as other Wi-Fi functions, so device manufacturers will likely be quick to cut redundant technologies.
Here's a quick animation that illustrates the functionality of Wi-Fi Direct: