A cross section of a willow bat/cleft/tree will reveal a series of paralel straws, this is unique in the willow among tree's. The moisture content can escape very quickly due to these open ends when cut hence the need to wax/varnish the ends as the cleft is sawn. In pressing you aim to harden a thin layer of the face by compression and this in essence flattens the straws and allows them to flex into the soft middle which upon return to shape gives the rebound.
The current Salix Alba varieties are selected for the low density in the Willow family. There is a range of denisty naturally occuring amongst any species. Each year of growth is laid down as a grain as with any tree and in simplistic terms the grain line is a level of stiffness. The more grains in the face the stiffer the blade. When it comes to pressing I'd say compare trying to press a layer of plastic straws, quite simple, but the stiffer material in the straw the harder it becomes to press without increasing the pressure, too much and the bat cracks.