The outermost electron orbitals of an atom where electrons are filled are valence bands.
When we excite an electron from the valence band electrons jump into the conduction band which makes the flow of electric current.
The bandgap is the gap between these bands.
In the case of conductors, the valence band overlaps the conduction band, so the excitation of electrons becomes very easy in the case of metals. So they can easily conduct electricity.
Examples of Conductor are Silver, Copper, Aluminium etc.
In the case of insulators, the bandgap between the valence band and conduction band is much high. So an electron can't jump from the valence band to the conduction band. So they do not conduct electricity.
Example of insulators is Carbon , Paper, Rubber etc.
In the case of semiconductors, the band gap between the valence band and conduction band is less. So electrons can jump when we give some energy. They lie in between the conductors and the insulators.
Examples of Semiconductors are Arsenic , Silicon, Germanium etc.