Why insulator can not conduct electricity?

In insulator, the atoms are electrically much stable. The other most shell of the atoms are completed. So there is no chance of gaining or loosing electron by these atoms. In other words, the forbidden band gap between valance band and conduction band is sufficient large in insulator.

The energy required by the electrons to cross over to the conduction band is impractically large. That is why insulators can not conduct electric current easily. Wood, Glass, Plastic, Mica are well known example of insulator.