In a word, reader Jan: steam. Expanding steam is the force that pushes apart those delicate sheets, which then crisp up in the heat of the oven. But of course to make steam you need water, so the logical question then becomes: where does the water come from? In part from the dough itself, but also from the butter.
Butter, depending on the type, is between ten and seventeen percent water. Considering that steam occupies about 1600 times the space that water does, that’s a heck of a lot of potential leavening power. Of course the amount of oomph will depend on how much butter you use, and that’s why makers of filo pies and pastries tend to be generous with the good stuff. Lots of lubrication plus lots of steam means lots of flake. Flavor too.