Burn changes the white point of the image so that less than max brightness objects will map to white. Here are three images all with exactly the same luminance data but different exposure (tone mapping) settings.
First, with no modifications to the tone mapping you can see that the average color maps to gray:
With the brightness cranked up to 0.4 we can get rid of some of the "grayness" of the image. Think of this as intentionally overexposing a photo a little:
Finally, adding some burn can really make a big difference in the brighter regions of the image-- in this case I used 0.5.
The amount of burn you'll use varies quite a bit from scene to scene - There are no good rules of thumb here.