What is the physical significance of the constant known as the
permittivity of free space?
It is basically the scale factor between the unit of force and
the unit of charge. There are actual electric and magnetic unit systems in
which there is no such factor (since it would be 1). For most of our
experiences we insist on measuring charge in coulombs and measuring forces (or
electric fields) in Newtons (Newtons per coulomb). The coefficient that we
need to make it come out right is related to the permittivity of free space.
The words probably go back to the days when we thought there was an ether in
space. You can also think about it as the way space effects the forces
between two charges. In this way it become s a property of space.