Difference between conductor and insulator :
In case of conductor the gap between the valence band and conductor band is very small or overlaps that's why under an applied electric field the conductor (metals) shows conductivity (electron can flow easily) whereas in insulator the gap between filled valence band and the next higher energy unoccupied band (conductions band) is large,electron cannot jump to it and such substance has very small conductivity and it behaves as an insulator.
