We know that an electric current can produce magnetic field in a nearby space; and in the opposite way, a magnetic field can produce an electric field that can drive a current. This kind of relation between a magnetic field and the electric field it induces is called Faraday’s law of induction.
An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing. If we move a magnet in and out of a loop, the number of magnetic field line changes when we move the magnet with respect to the loop. If we put another loop (Loop B) next to the loop (loop A), there are no field lines when the switch (on loop B) is open. Once switch (on loop B) is closed, current increases in loop A. This increases magnetic field through the loop A and B. Therefore the number of field lines passing through loop B changes.