The magnetic domains in the iron core align with the magnetic field created by the current in the primary coil. The field of the aligned iron atoms adds to that of the original field, making it even stronger. This increases the magnetic induction.
Work Step by Step
This is the principle behind electromagnets, and is discussed on page 459. Inserting an iron core in the secondary further increases the changing magnetic field through the secondary, and increases the secondary voltage. The core also guides more magnetic field lines through the coils of the secondary.