Kinect - or more correctly Kinect for Xbox 360 - is a device for interacting with the console without using a controller. The player's body "becomes" the controller.
Kinect uses a combination of infrared "structured light" and two cameras to detect the players position and movements. These movements are then interpreted by the software and either mapped directly to the players avatar or used as commands.
The Kinect also has a microphone so that games can interpret spoken commands.
Questions regarding 1) Kinect hardware and 2) intereaction with Kinect should use this tag. Questions regarding Kinect enabled games should not use this tag unless the question is regarding one of the 2 aforementioned subjects.