The models for insulators, semi-conductors and conductors are described by their atomic structures. Materials are basically classified in terms of their conductivities and the models explains why some materials conducts better or worst than most metals which basically accounts for conductors.
Electric field is generated by voltage source or battery. Electrons will be attracted by the positive charge at the positive potential terminal indicated by the “red" line.
If the electrons are tightly held by the nucleus’s positive charges, the externally applied charges or potential fail to move them. That’s the result of any insulators.
In conductors, there are lots of electrons which is not held by the nucleus at all, thus allow them to move to the externally applied potential.
In semi-conductors, and at room temperature, the valence electrons are gently freed from the nucleus and allow the flowing of them when external voltage is applied.