Why do we need to put PCB inside a (metal) box?

Shielding can be anything from using a coaxial or shielded cable, to a sealed conductive chamber for circuit isolation. Shielding serves a reciprocal purpose: it protects the circuit in it by shielding from outside noise or unwanted signals; and conversely, it contains its own signals and thus protects the outside world from interference of its own making. Shielding is mostly used to block electrostatic or "E" fields (Faraday shield). However, if ferrous metal (tempered Mu Metal works best for magnetic fields) is used then both electrostatic and some level of magnetic shielding is accomplished. This is especially useful where open frame transformers or unshielded coils are used and would otherwise exchange signals by mutual inductance.
When is a Shield a Shield?
One important requirement for a shield to be effective, is that there must be no currents flowing through the shield itself. This is best accomplished by connecting the reference or common, at only one point on the shield, thus preventing any flow of current. The reason for this, is that any current flowing in the shield material itself can produce secondary fields on the other side of the shielding material and thereby reducing the effectiveness of the shield. An extreme case of this might be a shielded cable, whose shield has a different potential at each end, and the resulting current flow in the shield, inducing unwanted noise into the center or shielded conductors. (In this situation one might find a remedy by disconnecting one or the other ends of the cable. However, this may not prove satisfactory in certain environments, and may require a "Guard" potential, which is some compromise potential.)

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