The faraday cage is a closed hull of a conductive material. When there are external electric fields the inner area remains field free because there a opposite field is created through electrostatic induction.
When a faraday cage is in an electric field, electrons gather at the side of the metal that faces the positive pol of the field. That leads (as described in the article electrostatic induction) to the creation of an electric field because on one side of the metal is positive excess charge and on the other side is a negative excess charge. This field is opposite to the outer field and the field lines cancel and there is no electric force in the inner of the farady cage.