How and in what kind of situations should it be used?
Most camera bodies (afiak) that display an image histogram, presents a histogram that is based on the JPEG representation of the RAW data captured by the camera sensor.
If you do your post processing work with RAW images (and you should ;) ), and you use the camera's histogram display as a guide when taking pictures, then the discrepancy between the histogram and the actual image may be enough to throw off your image (ie what you see, isn't what you get).
Some bodies allow you to use neutral parameters for contrast, saturation, and brightness which means the JPEG and RAW image are more closely matched (and by relation the histogram), but that still leaves the camera's whitebalance.
UniWB is a way to effectively cancel out the whitebalance, thus allowing for a more "true" histogram for your RAW image.
So what kind of situations should you use it? Well clearly if you're not shooting RAW, then there is not point. If you don't use the camera's histogram after taking the shot, then it makes no sense to use this.
When it does make sense is if you find that the RAW images you work with aren't what you expect, and you're looking for tweaks to make in your workflow to reduce the effort you spend in post processing to correct your images.
Or, if you are a crazy perfectionist that has to do everything imaginable to get the best, most perfect image possible, then this is worth investigating.
As Alan says, it's a way to get an in-camera histogram that more accurately represents the raw capture. So, the times when you would use it are when you are unsatisfied with the histograms you're getting.
The very long and detailed explanation from Guillermo Luijk is here: http://www.guillermoluijk.com/tutorial/uniwb/index_en.htm
For myself the easiest way to understand UniWB was the following.
Most current digital cameras have twice as much green light sensors as they have reds and blues (referenced as RGBG). Now to achieve neutral gray by changing white balance, usually the red and blue channels need to be amplified more than green. Just a few examples (for Canon 350D):
So when your camera generates JPG based histogram (where your in-camera white balance setting is taken into account regardless the fact you shoot RAW) under tungsten lightning, the blue channel will be shown as clipped far before it actually is. Same goes for red channel using Shade WB.
UniWB's main idea is to set all WB multiplier's to 1, so your histogram is as close to reality as possible and you can achieve optimal exposure.
To use UniWB, simply find a RAW file for your camera, download, copy to your memory card and set the camera's white balance using that photo (most of the modern cameras can set WB based on taken shot). Files for some cameras and a lot more theory can be found at the end of this page.
Be aware that the colors on your camera display will be way off and need correction during RAW conversion. When shooting with UniWB, you'd better use a color target as a reference.
Here is an example shot using UniWB before correction (RGB values of white square are 162, 253, 197):
And after correction (RGB values of white square are 236, 235, 235):