What property of the Ionoshpere causes waves to be reflected off it?

Answer 1

In a word 'Conductivity'
There are free electrons in the upper atmosphere which cause electrical conductivity but they keep colliding with neutral molecules which disrupts the conduction. At a certain height the air pressure is low enough for the electrons to remain free for a time greater or equal to the frequency of radio waves at at that height it becomes strongly conductive and behaves like a mirror.

Answer 2

The electrically charged ions act as reflectors for some of the wavelengths of the radio wave spectrum. A fine wire mesh also acts as a reflector (you would have seen antennae made of wire mesh).