This is easy to understand. Inside and on the surface of any conductor, there has to be a constant electrostatic potential because any gradient in this potential is an electric field that would lead to currents which cannot be sustained in an electrostatic situation. Thus in any conductor charges redistribute in such a way that there is always a zero electric field inside the conductor. In typical conductors like metals, with high concentration of charge carriers surface charges build up to produce the constant potential, and thus zero electric field, inside and along the surface.