What is an insulator?
It can be explained in two ways ,
According to this theory the overlapping of valence band and conduction band tells us about the conductivity of a substance, in insulators the valence band and the conduction band both are separated to a large distance which will cannot be over lapped by applying small energy .
If conduction band and valence band don't overlap there would be no exchange of electrons and in that case the material cannot conduct electricity or heat .
The conductivity of a element is wholly and solely dependent upon the presence of free electrons which which can move freely and conduct electricity . In insulators there are no free electrons and in that case it cannot conduct electricity.