The Channel Mixer is used for special effects, for color and black-and-white alike. The Channel Mixer is divided into three sections: Red, Green and Blue. Those sections represent the three available color output channels in a RGB image. All values shown here are percentages. The mixer makes a new R channel from the specified percentages of the existing R, G, and B channels; similarly for the other channels.
The Channel Mixer can be used to adjust the white balance of the photo, if the proper White Balance tool does not suffice. For the sliders that have a starting value of 100, enter values other than 100 and you are in effect changing the white balance (i.e. only changing the R slider on the R channel, only the G slider on the G channel, and only the B slider on the B channel). Get the image into the right ballpark, then use the Temperature/Tint sliders of the usual White Balance tool to fine tune. In principle this allows an arbitrary range for White Balance.