This is a common advertising pitch that is quite a bit oversimplified.
Originally Posted by mporter012
Much distance haze and mist/fog is made up of water vapor and pollutants that absorb a lot of the red and green light striking/passing through it and reflects/passes mostly blue. This means that IF there are objects in the scene that are illuminated by another light source (say, the sun) and you use a blue filter, the haze/mist/fog that is mostly blue will be rendered lighter than "normal" (i.e., what you see).
If, however, the entire scene is foggy, and the only illumination you have is being filtered through the fog (such as on a foggy day on the coast while you're on the beach), then there is no difference in color to be had; everything is relatively bluer compared to daylight (much like shooting in open shade) and your blue filter will simply affect overall exposure less predictably (i.e., your filter factor will be different than for daylight). This will likely result in a slight overexposure if you apply the daylight factor, but will NOT render the fog much lighter relative to other neutral subjects (which are all illuminated by the same color light).
So, use the blue filter to lighten and "enhance" distance haze and mist/fog in scenes that have other general illumination sources (say, a scene of rolling hills with mist and haze in the distance). The approximate opposite of this is using a yellow filter to reduce the effect of distance haze in landscapes.
However, when photographing in the fog itself where there is only light filtered by the fog, your blue filter will have little effect on contrast. It is better to deal with this delicate rendering by controlling contrast using standard exposure/development controls guided by careful visualization of how you want to render the fog (this is a bit tricky for many).
Hope this helps,