The common explanation I often read is that it increases tension. But if it increases tension, then it also increases pitch (pitch is mainly a product of tension, mass, and length) so you would tune down to where the tension was the same as before the adjustment... so that doesn't really make sense to me.
So I would guess that the main factors are 1) with higher action, less vibrations are lost to the fingerboard and 2) you can dig in a little harder.
But, I'm no expert, and someone might have better information.
http://www.talkbass.com/forum/showpost.php?p=720998&postcount=10
my understanding is that there are two kinds of tension (or pressure) we are talking about here - the tension along the length of the string and the pressure on the top plate. raising the string height or lowering the saddle will put more pressure on the top plate, meaning (in many cases) more overall volume.
