When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic equilibrium. The resulting charge distribution and its electric field have many interesting properties, which can be investigated with the help of Gauss's law.
Suppose a piece of metal is placed near a positive charge. The free electrons in the metal are attracted to the external positive charge and migrate freely toward that region. This region then has an excess of electrons over protons in the atoms while the region from where the electrons have migrated has more protons than electrons. Consequently, the metal develops a negative region near the charge and a positive region at the far end. This separation of equal magnitude and opposite type of electric charge is called polarization. The electrons migrate back and neutralize the positive region if the external charge is removed. The polarization of the metal happens only in the presence of external charges.
When a conductor is polarized, an induced electric field is created inside the conductor opposite to the external field. This means that the net field inside the conductor differs from the field outside, and is a vector sum of the fields due to external charge and induced surface charge densities. The free electrons continuously migrate under the external electric field until the induced electric field becomes equal in magnitude to the external field and electrostatic equilibrium is established. Thus, the net electric field inside the conductor at electrostatic equilibrium is zero. From Gauss's law, if the net electric field inside a conductor is zero, then there is no net charge enclosed by a Gaussian surface that is solely within the volume of the conductor. Thus, the net charge inside the conductor is also zero.
