Peter,

They do 3 things that I can think of instantly.

1. They improve ventilation.  May not be connected but I see less chalkbrood
with a mesh floor.

2. The living mites that drop to the floor keep falling.  This apparently is
between 17% and 57%.  Dr Jeff Pettis has experimentally shown that if there
is a gap of at least 2" between the mesh floor and any solid floor they don't
get back on the bees. Les than that distance and they do. At half inch space
they all get back.

3. They enable a tray to be slid in for a 24 hour natural mite drop check
this enables the beekeeper to determine whether or not to treat.  Less
treatments = delayed resistance.

Chris