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Here you see a Faraday cage. It is a conducting hollow box in an external electric field \(E\). Since the box is conductive, electrons can move freely on its surface. In an electric field, the electrons move opposite to the direction of the external field (this effect is called electrostatic induction). On the other side of the box there is electron deficiency, therefore this side is positively charged.
Because of this charge separation, another electric field is created inside the box. The magnitude of this field is the same as of the external field, and the two fields point in opposite directions. They cancel each other out inside the box. So the internal region of the box is field-free.