It is based on the observation that the RGB histogram is created from the image data after applying white balance, whereas for anyone shooting RAW the interesting data is whether there is any white clipping before applying white balance. UniWB is about setting the white balance to the closest value to "no white balance" that the camera supports. Since white balance can be represented by multiplying the red and blue channels by a constant while leaving the green channel un-multiplied, "no white balance" would have the multipliers 1.0 for red and blue - thus the name "uni"-white balance.
Guillermo Luijk has a great page where you can find instructions on how to set up UniWB[b] on your camera, along with settings files you can download. I was not aware of it when I wrote this, so the settings I chose for my Nikon D600 were: 4760K and G6. At that point the red multiplier is 1.23 and the blue is 1.18 which is close enough for government work. A consequence of these settings is that the image comes out looking horrible:
However, since we are shooting RAW, this can be fixed in post-processing. For those of us who regularly find the camera's automatic white balance giving the wrong results and set it in post anyway, this is a trivial price to pay in order to get more useful histograms and being able to expose more to the right.