The Background Color section in the Camera Device allows adjusting the red / green / blue / alpha channels for the main background from the resulting texture rendered by the camera (the so called render target). More information about the render target can be found in the chapter Video Processing Pipeline, a possible application for adjusting the background color could be blacklevel compensation when working with multi-softedged projection(s).
If you are not familiar how to use the color picker tool, please read the topic "Adding, Editing and Removing FX".
You can control the color parameters externally, simply assign a value between 0-255 to each color or alpha parameter.
For DMX control, the chapter DMX Tables lists all parameter information, for other external control e.g. via the Widget Designer the Parameter List is of interest.